Physics Unit Conversions and Formulas
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Questions and Answers

What is the area of a rectangle calculated by?

  • length * width (correct)
  • length + width
  • 2 * (length + width)
  • length / width

    • Which formula correctly represents the area of a triangle?

  • Area = (1/2) b * h (correct)
  • Area = b + h
  • Area = b * h
  • Area = 2 * (b + h)

    • To calculate the volume of a cylinder, which formula is used?

  • V = π * r^2 * h (correct)
  • V = π * r * h^2
  • V = 2 * π * r * h
  • V = r^2 * h

    • What constant represents the acceleration due to gravity in ft/sec²?

    <p>32.2 ft/sec²</p> Signup and view all the answers

    Which unit is equivalent to 1 rem?

    <p>10-2 sievert</p> Signup and view all the answers

    The area of a circle is calculated using which formula?

    <p>Area = π * r^2</p> Signup and view all the answers

    What value does Avogadro's number approximate?

    <p>6.024 x 10^23</p> Signup and view all the answers

    1 footcandle is equivalent to how many lux?

    <p>10.76</p> Signup and view all the answers

    What is the relationship between force, mass, and acceleration described by Newton's second law?

    <p>F = ma/g</p> Signup and view all the answers

    What formula represents the work done when a force is applied over a distance?

    <p>W = FS</p> Signup and view all the answers

    Which equation represents the final velocity of an object given its initial velocity, acceleration, and time?

    <p>v = v0 + at</p> Signup and view all the answers

    If a compressed spring exerts a force, what type of force is this categorized as?

    <p>Spring Force</p> Signup and view all the answers

    When calculating frictional force, which of the following values is used in the equation F = μN?

    <p>Normal Force</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>V = (4/3)πr^3</p> Signup and view all the answers

    How is the volume of a pyramid determined?

    <p>V = (1/3)Bh</p> Signup and view all the answers

    What fundamental relationship is expressed by the Pythagorean theorem?

    <p>C^2 = a^2 + b^2</p> Signup and view all the answers

    What does Hooke's law describe?

    <p>The energy stored in an elastic material when it is stretched</p> Signup and view all the answers

    What is the unit of force defined by the International System of Units?

    <p>Newton</p> Signup and view all the answers

    What does kinetic energy depend on?

    <p>Mass and speed</p> Signup and view all the answers

    What characterizes elastic potential energy?

    <p>Energy stored when materials are compressed or stretched</p> Signup and view all the answers

    How do you calculate the potential energy of an object?

    <p>PE = mgh</p> Signup and view all the answers

    Which of the following represents the correct relationship of sides in a triangle based on the sine rule?

    <p>A/SinA = b/Sinb = c/Sinc</p> Signup and view all the answers

    What does the acceleration of an object relate to regarding force?

    <p>It is directly proportional to the force applied</p> Signup and view all the answers

    What is the equivalent of 1 bar in psi?

    <p>14.5 psi</p> Signup and view all the answers

    How many grams are in one pound?

    <p>454 grams</p> Signup and view all the answers

    What is the conversion factor for 1 gallon to liters?

    <p>3.785 liters</p> Signup and view all the answers

    What is the relationship between Celsius and Kelvin temperature scales?

    <p>K = C + 273</p> Signup and view all the answers

    How many ounces are there in one pound?

    <p>16 ounces</p> Signup and view all the answers

    What is the conversion rate for pounds to kilograms?

    <p>0.454 kg</p> Signup and view all the answers

    Which unit can be converted to 1000 mg?

    <p>1 gram</p> Signup and view all the answers

    What is the metric equivalent of 1 ton (US)?

    <p>2200 kg</p> Signup and view all the answers

    What is the value of 1 Nm² in psi?

    <p>0.1450 psi</p> Signup and view all the answers

    How many liters are in 1 cubic meter (m³)?

    <p>1000 liters</p> Signup and view all the answers

    What does the null hypothesis state regarding the populations being studied?

    <p>Any observed differences are due to sampling or experimental error.</p> Signup and view all the answers

    What is a Type I error in hypothesis testing?

    <p>Rejecting the null hypothesis when it is true.</p> Signup and view all the answers

    What does the Coefficient of Variation (CV) measure?

    <p>The ratio of standard deviation to the mean.</p> Signup and view all the answers

    In the context of cumulative error, which type of error is NOT mentioned as common in air sampling?

    <p>Statistical design errors</p> Signup and view all the answers

    Which of the following is true regarding precision and accuracy?

    <p>Accuracy indicates how close a measurement is to an accepted value.</p> Signup and view all the answers

    What does a lower confidence limit (LCL) help determine in a compliance context?

    <p>If the measured value exceeds the permissible exposure limit (PEL).</p> Signup and view all the answers

    What is indicated by a Type II error in hypothesis testing?

    <p>Failing to detect a difference when one actually exists.</p> Signup and view all the answers

    What does the 95% confidence level signify in hypothesis testing?

    <p>The confidence interval contains the true parameter 95% of the time.</p> Signup and view all the answers

    Which aspect does not directly impact the coefficient of variation?

    <p>Sample size</p> Signup and view all the answers

    What is the primary concern of measurement errors in cumulative error analysis?

    <p>Accuracy of calibration and instrument measurements.</p> Signup and view all the answers

    What is the SI equivalent of 1 rad?

    <p>0.01 gray</p> Signup and view all the answers

    Which of the following represents the correct unit conversion for density?

    <p>1 gm/cm³ = 62.4 lb/ft³</p> Signup and view all the answers

    How can the area of a square be computed?

    <p>Area = side²</p> Signup and view all the answers

    Which formula is used to determine the volume of a rectangular solid?

    <p>V = l × w × h</p> Signup and view all the answers

    What is the formula for calculating the area of a triangle?

    <p>Area = (1/2)b × h</p> Signup and view all the answers

    Which of the following correctly states the conversion for the velocity of light?

    <p>3.0 x 10⁸ m/sec</p> Signup and view all the answers

    Which of the following equations represents the correct relationship of area in a circle?

    <p>Area = πr²</p> Signup and view all the answers

    What is the formula for calculating the volume of a cylinder?

    <p>V = πr²h</p> Signup and view all the answers

    What does the null hypothesis typically state about the populations being studied?

    <p>The observed difference is due to sampling or experimental error.</p> Signup and view all the answers

    What can a Type I error lead to in hypothesis testing?

    <p>Rejecting a true null hypothesis.</p> Signup and view all the answers

    What is indicated by a Type II error in hypothesis testing?

    <p>Failing to reject a false null hypothesis.</p> Signup and view all the answers

    How is the Coefficient of Variation (CV) calculated?

    <p>Standard deviation divided by the mean.</p> Signup and view all the answers

    What does a lower confidence limit (LCL) help to determine in compliance?

    <p>Compliance with the permissible exposure limits.</p> Signup and view all the answers

    What is the primary purpose of cumulative error analysis?

    <p>To calculate the upper and lower confidence limits.</p> Signup and view all the answers

    In terms of precision and accuracy, how is accuracy defined?

    <p>How close a measurement is to the actual value.</p> Signup and view all the answers

    What does a coefficient of variation (CV) reflect about a dataset?

    <p>The dispersion relative to the mean.</p> Signup and view all the answers

    What does a 95% confidence level imply in hypothesis testing?

    <p>There is a 95% chance that the observed results are due to chance.</p> Signup and view all the answers

    What does the term 'precision' refer to in measurement analysis?

    <p>The consistency of repeated measurements.</p> Signup and view all the answers

    What is the equivalent of 1 bar in terms of atm?

    <p>0.9869 atm</p> Signup and view all the answers

    How many grams are in 1 pound?

    <p>454 grams</p> Signup and view all the answers

    What is the weight of 1 gallon of water in pounds?

    <p>8.34 lb</p> Signup and view all the answers

    How many liters are there in 1 gallon?

    <p>3.785 liters</p> Signup and view all the answers

    What is the conversion ratio of 1 ton (US) to pounds?

    <p>2000 pounds</p> Signup and view all the answers

    What is the formula for calculating the volume of a sphere?

    <p>V = (4/3)πr^3</p> Signup and view all the answers

    What is the relationship expressed by the formula for converting Fahrenheit to Celsius?

    <p>°C = 9(°F − 32)/5</p> Signup and view all the answers

    What is the equivalent of 1 mm Hg in psia?

    <p>0.01934 psia</p> Signup and view all the answers

    How is the volume of a pyramid determined?

    <p>V = (1/3) × B × h</p> Signup and view all the answers

    How many ounces are in 1 pound?

    <p>16 ounces</p> Signup and view all the answers

    What principle does Hooke's law illustrate regarding springs?

    <p>There is no elastic potential energy if the spring is compressed.</p> Signup and view all the answers

    What is the pressure equivalent of 1 atm in psi?

    <p>14.7 psi</p> Signup and view all the answers

    Which equation represents the relationship between the sides of a right triangle in trigonometry?

    <p>A/SinA = b/SinB</p> Signup and view all the answers

    What is the volume equivalent of 1 liter in milliliters?

    <p>1000 ml</p> Signup and view all the answers

    What is the equation for kinetic energy?

    <p>KE = 1/2 mv^2</p> Signup and view all the answers

    What does potential energy depend on?

    <p>Mass and height above a reference point</p> Signup and view all the answers

    Which of the following correctly defines a newton?

    <p>The amount of force required to give a 1-kg mass an acceleration of 1 m/s^2</p> Signup and view all the answers

    What characterizes elastic potential energy?

    <p>Energy stored in materials as they are stretched or compressed</p> Signup and view all the answers

    Which of the following formulas is used to calculate the force?

    <p>F = m × a</p> Signup and view all the answers

    In the context of the Pythagorean theorem, which statement is true?

    <p>The square of the hypotenuse is equal to the sum of the squares of the two shorter sides.</p> Signup and view all the answers

    What is the formula used to calculate work done when a force is applied over a distance?

    <p>W = F * S</p> Signup and view all the answers

    Which equation correctly describes the relationship between final velocity, initial velocity, acceleration, and time?

    <p>v = v0 + at</p> Signup and view all the answers

    What type of force is exerted by a compressed or stretched spring?

    <p>Spring force</p> Signup and view all the answers

    Which of the following represents the equation used to calculate frictional force?

    <p>F = μN</p> Signup and view all the answers

    How is tension force defined in relation to other forces?

    <p>It is the force required to pull an object.</p> Signup and view all the answers

    What unit is used to measure the radioactivity of a substance?

    <p>Curie</p> Signup and view all the answers

    In the context of light measurement, what does 1 footcandle equal in terms of lux?

    <p>10.76 lux</p> Signup and view all the answers

    Which of the following constants is equal to Planck's constant?

    <p>6.626 x 10^-34 J-sec</p> Signup and view all the answers

    When calculating the area of a circle, what does π represent?

    <p>Ratio of circumference to diameter</p> Signup and view all the answers

    What is the unit for measuring the intensity of luminescence in a solid angle?

    <p>Candlepower</p> Signup and view all the answers

    Which formula represents the calculation for the volume of a prism?

    <p>V = A × h</p> Signup and view all the answers

    What is equivalent to 1 gray in terms of radiation absorption?

    <p>0.01 sievert</p> Signup and view all the answers

    In the context of density, what does 1 gm/cm³ equal in slugs/ft³?

    <p>1.94 slugs/ft³</p> Signup and view all the answers

    How is the tension force characterized in relation to other forces?

    <p>It pulls an object, opposing the effects of compression.</p> Signup and view all the answers

    What is required to calculate the frictional force acting on a surface?

    <p>The coefficient of friction and the normal force acting on the surface.</p> Signup and view all the answers

    What does the equation F1D1 = F2D2 signify in the context of forces and distances?

    <p>The equilibrium state of forces acting on a system.</p> Signup and view all the answers

    When calculating the work done on an object, which factors must be considered?

    <p>The force applied and the distance over which it acts.</p> Signup and view all the answers

    In the equation for final velocity $v = v_0 + at$, what does each term represent?

    <p>$v$ is the final velocity, $v_0$ is the initial velocity, and $a$ is acceleration.</p> Signup and view all the answers

    What does the null hypothesis (H0) state in hypothesis testing?

    <p>The observed difference is due to experimental error.</p> Signup and view all the answers

    Which of the following best describes Type I error?

    <p>Rejecting the null hypothesis when it is true.</p> Signup and view all the answers

    How is the Coefficient of Variation (CV) calculated?

    <p>Standard deviation divided by the mean, times 100.</p> Signup and view all the answers

    What does a lower confidence limit (LCL) indicate in compliance analysis?

    <p>The result is compliant if LCL is greater than the PEL.</p> Signup and view all the answers

    What does accuracy refer to in the context of measurements?

    <p>The closeness of measurements to the accepted value.</p> Signup and view all the answers

    In the context of cumulative error, which factor is most likely to affect the upper and lower confidence limits?

    <p>Calibration errors in instruments.</p> Signup and view all the answers

    What does Type II error signify in hypothesis testing?

    <p>Failing to reject the null hypothesis when it is false.</p> Signup and view all the answers

    How is the concept of the coefficient of variation (CV) beneficial in data analysis?

    <p>It provides a standardized measure of dispersion relative to the mean.</p> Signup and view all the answers

    Why is the 95% confidence level significant in hypothesis testing?

    <p>It reflects a high likelihood that true results fall within the confidence interval.</p> Signup and view all the answers

    Which term describes the relationship between accuracy and precision in measurements?

    <p>Precision does not ensure accuracy.</p> Signup and view all the answers

    How is the volume of a pyramid determined?

    <p>V = (1/3) × B × h</p> Signup and view all the answers

    What does Hooke's law indicate about springs?

    <p>The force is proportional to the amount of stretch or compression.</p> Signup and view all the answers

    Which equation shows the relationship in a right triangle for finding a side using the cosine function?

    <p>C² = a² - 2ab cos(θ)</p> Signup and view all the answers

    What characterizes kinetic energy in relation to an object's speed?

    <p>It increases with the square of the speed.</p> Signup and view all the answers

    In the context of energy types, which statement best defines elastic potential energy?

    <p>Energy stored due to the stretching or compressing of materials.</p> Signup and view all the answers

    Which formula accurately represents the volume of a sphere?

    <p>V = (4/3)πr³</p> Signup and view all the answers

    What does potential energy depend on?

    <p>The mass of the object and its position relative to other masses.</p> Signup and view all the answers

    In the context of force, what does a newton represent?

    <p>The force required to accelerate a 1-kg mass at 1 m/s².</p> Signup and view all the answers

    What is a characteristic of the sine rule in trigonometry?

    <p>It relates angles to their opposite sides in any triangle.</p> Signup and view all the answers

    Which of the following is NOT a factor in calculating elastic potential energy?

    <p>The shape of the object.</p> Signup and view all the answers

    What is the equivalent value of 1 bar in atmospheres?

    <p>1.01325 atm</p> Signup and view all the answers

    Which of the following represents the mass equivalent of 1 US ton?

    <p>2000 lb</p> Signup and view all the answers

    What conversion factor is used to convert pounds to kilograms?

    <p>2.205</p> Signup and view all the answers

    How many milliliters are in 1 fluid ounce?

    <p>29.57 ml</p> Signup and view all the answers

    What is the relationship between Celsius and Kelvin temperatures?

    <p>K = C + 273.15</p> Signup and view all the answers

    Which of the following is true regarding pressure in psi?

    <p>1 bar = 14.5 psi</p> Signup and view all the answers

    Which of the following conversions correctly describes 1 mm Hg in psia?

    <p>0.01934 psia</p> Signup and view all the answers

    How many grams are in 1 ounce?

    <p>28.35 grams</p> Signup and view all the answers

    What is the value of 1 liter in cubic feet?

    <p>0.03531 ft³</p> Signup and view all the answers

    Which unit conversion represents the volume of 1 gallon in liters?

    <p>3.785 liters</p> Signup and view all the answers

    What is the unit equivalent to 1 curious in radiation measurements?

    <p>3.7 x 10^10 disintegrations/sec</p> Signup and view all the answers

    Which of the following correctly represents the acceleration due to gravity in metric units?

    <p>9.8 m/sec²</p> Signup and view all the answers

    Which formula represents the volume of a cylinder?

    <p>V = πr^2h</p> Signup and view all the answers

    What does 1 gm/cm³ convert to in terms of weight density?

    <p>62.4 lb/ft³</p> Signup and view all the answers

    Which of the following represents the relationship between candela and lux?

    <p>1 candela = 1 lumen/steradian</p> Signup and view all the answers

    What is Planck's constant value in scientific notation?

    <p>6.626 x 10^-34 J-s</p> Signup and view all the answers

    For which shape is the formula Area = s^2 used?

    <p>Square</p> Signup and view all the answers

    Which formula calculates the area of a triangle?

    <p>Area = 1/2 b * h</p> Signup and view all the answers

    What formula correctly represents the volume of a sphere?

    <p>V = (4/3)πr³</p> Signup and view all the answers

    Which formula is used to calculate the volume of a pyramid?

    <p>V = (1/3)Bh</p> Signup and view all the answers

    In terms of energy, what is kinetic energy dependent on?

    <p>Mass and velocity</p> Signup and view all the answers

    What does Hooke's law state about springs?

    <p>The force exerted is proportional to the distance compressed</p> Signup and view all the answers

    Which equation represents the relationship in a right triangle based on trigonometric functions?

    <p>A/SinA = b/Sinb = c/Sinc</p> Signup and view all the answers

    What type of energy is stored in materials like springs when they are stretched or compressed?

    <p>Elastic Potential Energy</p> Signup and view all the answers

    What does potential energy depend on for an object?

    <p>Mass and height</p> Signup and view all the answers

    What is the unit of force defined by the International System of Units?

    <p>Newton</p> Signup and view all the answers

    According to the relationship described in physics, how is force related to mass and acceleration?

    <p>Force equals mass times acceleration</p> Signup and view all the answers

    Which equation describes the elastic potential energy stored in a spring?

    <p>PE = 1/2 kx²</p> Signup and view all the answers

    What is the conversion factor from pounds to kilograms?

    <p>0.454</p> Signup and view all the answers

    What is the relationship between pressure and atmospheric units?

    <p>1 atm = 0.98 bar</p> Signup and view all the answers

    How many grams are in one ounce?

    <p>28.35 g</p> Signup and view all the answers

    What is the equivalent of 1 liter in milliliters?

    <p>1000 ml</p> Signup and view all the answers

    Which of the following correctly converts 1 bar to psi?

    <p>14.7 psi</p> Signup and view all the answers

    What is the temperature conversion formula from Fahrenheit to Celsius?

    <p>°C = (°F − 32) × 5/9</p> Signup and view all the answers

    How many cubic feet are in 1 gallon?

    <p>0.028 ft³</p> Signup and view all the answers

    What is the conversion of 1 mm Hg to psia?

    <p>0.01934 psia</p> Signup and view all the answers

    What is the conversion factor for 1 gallon of water in pounds?

    <p>8.34 lb</p> Signup and view all the answers

    How many ounces are in 1 pound?

    <p>16 oz</p> Signup and view all the answers

    What is the unit of force as defined by the International System of Units?

    <p>Newton</p> Signup and view all the answers

    Which equation describes the relationship between force, mass, and acceleration?

    <p>F = ma/g</p> Signup and view all the answers

    What does the variable 'μ' represent in the equation for calculating frictional force?

    <p>Coefficient of friction</p> Signup and view all the answers

    In the equation for calculating work done, which variables are multiplied together?

    <p>Force and distance</p> Signup and view all the answers

    Which of the following equations can be used to calculate the final velocity of an object given its initial velocity, acceleration, and time?

    <p>v = vo + at</p> Signup and view all the answers

    What does the null hypothesis (H0) indicate regarding the populations being studied?

    <p>There is no difference between the means of the populations.</p> Signup and view all the answers

    Which error occurs when the null hypothesis is rejected, but it is actually true?

    <p>Type I error</p> Signup and view all the answers

    What does the Coefficient of Variation (CV) indicate?

    <p>The dispersion of data relative to the mean.</p> Signup and view all the answers

    What does a Type II error signify in hypothesis testing?

    <p>Accepting the null hypothesis when it should be rejected.</p> Signup and view all the answers

    How does cumulative error typically affect sampling results?

    <p>It reduces the validity of confidence limits.</p> Signup and view all the answers

    What is described by the lower confidence limit (LCL) in a compliance context?

    <p>The minimum bound for the true mean estimate.</p> Signup and view all the answers

    How is precision defined in the context of measurement?

    <p>The degree to which repeated measurements yield the same result.</p> Signup and view all the answers

    What does the 95% confidence level imply about results?

    <p>There is a 95% chance that the true mean is within the confidence intervals.</p> Signup and view all the answers

    Which aspect is NOT directly related to the coefficient of variation (CV)?

    <p>Number of samples analyzed.</p> Signup and view all the answers

    What does the term 'sampling error' refer to in hypothesis testing?

    <p>Variability in estimates caused by selecting a subset from a population.</p> Signup and view all the answers

    Study Notes

    Radiation Units

    • Gray (Gy): 1 rad = 10^-2 Gy
    • Sievert (Sv): 1 rem = 10^-2 Sv
    • Curie (Ci): 1 Ci = 3.7 x 10^10 Bq
    • Becquerel (Bq): 1 Bq = 1 disintegration/sec

    Density of Water

    • 1 gm/cm3 = 1.94 slugs/ft3
    • Weight density = 62.4 lb/ft3

    Light

    • Candela: 1 candela = 1 lumen/steradian
    • Foot-candle: 1 footcandle = 10.76 candela/m2 = 10.76 lux

    Physical Constants

    • Acceleration of gravity: 32.2 ft/sec2 = 9.8 m/sec2
    • Velocity of light: 3.0 x 10^8 m/sec
    • Planck's constant: 6.626 x 10^-34 J·sec
    • Avogadro's number: 6.024 x 10^23/gram-mole

    Boolean Postulates

    • Area:
      • Rectangle: Area = length * width
      • Square: Area = s2, where s = side
      • Triangle: Area = (1/2) b * h, where b = base and h = height
      • Circle: Area = π * r2, where r = radius
    • Volume:
      • Rectangular Solid/Cuboid: V = l x w x h
      • Cube: V = a3, where a = Length of Edge
      • Cylinder: V = πr2h
      • Prism: V = B x h, where B = Area of base and h = Height
      • Sphere: V = (4/3)πr3
      • Pyramid: V = (1/3) x B x h, where B = area of base and h = height

    Trigonometric Functions

    • Right Triangle Definitions for Trigonometric Functions:
      • c2 = a2 + b2 – 2ab cos 0C
      • A/SinA = b/Sinb = c/Sinc

    Kinetic Energy

    • KE = 1/2mv2
      • m = mass of the object
      • v = speed of the object (velocity)

    Potential Energy

    • PE = mgh
      • m = mass of the object
      • g = acceleration due to gravity
      • h = height of the object

    Elastic Potential Energy

    • Hooke's Law:
      • Energy stored in elastic materials as the result of their stretching or compressing
      • The spring is said to be at its equilibrium position when it is not stretched or compressed

    Force

    • A newton (N): is the amount of force required to give a 1-kg mass an acceleration of 1 m/s2.

    Parameters

    • Parameters describe characteristics of a population.
    • They summarize the data and the entire population.

    Null Hypothesis

    • There is no significant difference between populations.
    • Any observed difference is due to sampling or experimental errors.
    • Represented as H0= M1=M2, meaning no difference between population means.
    • Used in conjunction with a 95% confidence interval, which means there is a 95% chance of the observed difference being true.

    Type I Error (False Positive- Alpha)

    • Occurs when you reject the null hypothesis when it is true.
    • You should accept the null hypothesis in this case.
    • Indicates a difference between means when there is actually no difference.

    Type II Error (False Negative - Beta)

    • Occurs when you fail to reject a false null hypothesis.
    • There is an actual difference in means, but you accept the null hypothesis.
    • You should reject the null hypothesis in this case.

    Coefficient of Variation (CV)

    • A measure of dispersion of a probability or frequency distribution.
    • Defined as the ratio of the standard deviation (SD) to the mean.
    • Represented as S/Xmean = %.

    Cumulative Error

    • Used to calculate the upper and lower confidence limits for air sampling.
    • Accounts for common errors like calibration, lab, instrument measurement, and correction errors during sampling and calculation.
    • As sample size increases, the result and assessment of the mean are enhanced.

    Precision and Accuracy

    • Accuracy refers to how close a measurement is to the actual or accepted value.
    • Accuracy is evaluated using the F-test.
    • *Precision represents the variability of repeated measurements.
    • Indicates the standard deviation (SD) of repeated measurements of the same true or accepted value using the same method.

    Lower Confidence Limit (LCL)

    • Used by OSHA officers to determine if a measured value exceeds the Permissible Exposure Limit (PEL).
    • If LCL > PEL: noncompliance.
    • If PEL > LCL: compliance
    • Overexposure is indicated when the time-weighted average (TWA) or PEL exceeds 1 and the LCL exceeds PEL.

    Units and Conversions

    • Pressure

      • 1 bar = 14.5 PSI = 0.98 atm = 760 mm Hg = 10^5^ N/m^2^*
      • 1 psia = 51.72 mm Hg
      • 1 psig = 14.7 psia
      • 1 mm Hg (Torr) = 0.01934 psia

    • Mass and Weight

      • 16 ounces (oz) = 1 lb
      • 1 g = 1000 mg
      • 2.205 lb = 1 kg
      • 1 ton (US) = 2000 lb
      • 1 tonne (Metric ton) = 1000 kg
      • 1 dram = 1771.85 mg

    • Heat Capacity

      • 1 bar = 100 cal/g/°C = 1 Btu/lb/°F
      • 1 kN/m2 = 0.1450 psia
      • 1 bar = 1 ppm = 1 mg /L
      • 1 kN/m2 = 0.009869 atm
      • 1 bar = 1 mg/m3 = 1 × 10−9 g/cm3
      • 1 g/cm3 = 1 × 109 mg/m3
      • 1 g/m3 = 62.42 lb/ft3 = 1 cal/g/°C
      • 1 Btu/lb/°F = 0.01602 g/cm3 = 4187 J/kg·K

    • Force, Pressure, or Stress

      • 1 pound-force = 4.45 newtons
      • 1 pound-force/square inch = 6.89 kilopascals

    • Illumination

      • 1 foot-candle = 10.76 lux
      • 1 foot-lambert = 3.426 candela/square meter

    • Length, Area, and Volume

      • 1 inch = 25.4 millimeters
      • 1 foot = 0.305 meters
      • 1 yard = 0.914 meters
      • 1 mile = 1.61 kilometers
      • 1 square inch = 645.2 square millimeters
      • 1 square foot = 0.093 square meters
      • 1 square yard = 0.836 square meters
      • 1 acre = 0.405 hectares
      • 1 square mile = 2.59 square kilometers
      • 1 fluid ounce = 29.57 milliliters
      • 1 gallon = 3.785 liters
      • 1 cubic foot = 0.028 cubic meters
      • 1 cubic yard = 0.765 cubic meters
      • 1 ounce = 28.35 grams
      • 1 pound = 0.454 kilograms
      • 1 liter = 1000 cm^3^
      • 1 liter = 1000 ml
      • 1 m^3^ = 1000 liter
      • 1 liter = 1.06 qt = 61.02 in^3^ = 0.03531 ft^3^
      • 1 ml = 1 cm^3^
      • 1 ft^3^ = 7.5 gallons
      • 1 gallon of water = 8.34 lb
      • 1 gallon = 3.78 liters
      • 1 liter = 61.02 cu in
      • 1 hour= 3600 seconds

    • Temperature

      • Fahrenheit to Celsius: 5(°F − 32)/9
      • Celsius to Fahrenheit: 9(°C + 32)/5
      • Celsius to Kelvin: °C + 273
      • Fahrenheit to Rankine: °F + 460

    • Other

      • 1% by volume = 10,000 ppm
      • STP (Standard Temperature and Pressure) = 25°C and 1 atm
      • 1 tesla = 10,000 gauss
      • 1 becquerel = 1 disintegration/s
      • 1 kg = 2.2 lb
      • 1 lb = 454 gram
      • 1 ton (US) =2000 lb
      • 1 atm = 14.7 psi = 760 mm Hg = 33.90 ft.

    Forces

    • Tension forces are required to pull an object, acting in the opposite direction to compression forces.
    • Spring force is exerted by a compressed or stretched spring.
    • Normal force (N) acts perpendicular to a surface and is equal to the force acting on the surface.
    • Frictional force acts parallel to a surface and opposes motion.
    • Coefficient of friction (μ) is a dimensionless quantity representing the ratio of frictional force to normal force.
    • Friction force (F) can be calculated using the formula: F = μN.
    • Newton (N) is the unit of force, with 1 N = 1 kg*m/s².
    • 1 kg is equal to 2.2 lb.
    • When considering an angle, the formula for friction force becomes Nsin θ + μ * N cos θ, where θ is the angle.

    Force and Distance

    • Work done is calculated by multiplying force (F) by distance (S): W = FS.

    Momentum

    • Momentum is a measure of mass in motion.

    Velocity

    • Velocity (v) can be calculated using the formula: v = v₀ + at.
      • v₀ is the initial velocity.
      • a is the acceleration.
      • t is the time.

    Distance

    • Distance (s) can be calculated using one of two formulas:
      • s = v₀t + ½ at²
      • v² = v₀² + 2as

    Work done

    • Work done (W) is measured in Joules (J).

    Newton's Second Law

    • Newton's Second Law states the relationship between force (F), mass (m), and acceleration (a): F = ma/g.
      • g is the acceleration due to gravity, approximately 9.8 m/s² or 32.2 ft/s².

    Force at an Angle

    • When a force acts at an angle to the horizontal, the horizontal component of the force is used to calculate work done.
    • For example, if a force acts at 30° to the horizontal and displaces an object 3 m horizontally, the work done is the horizontal component of the force multiplied by the displacement.

    Radiation Units

    • 1 rad is equal to 10^-2 gray.
    • 1 rem is equal to 10^-2 sievert.
    • 1 curie is equal to 3.7 x 10^10 becquerel.
    • 1 becquerel is equal to 1 disintegration per second.

    Density of Water

    • The density of water is 1 gm/cm3.
    • This is equivalent to 1.94 slugs/ft3.
    • Weight density is 62.4 lb/ft3.

    Light Units

    • 1 candela is equivalent to 1 lumen/steradian.
    • 1 footcandle is equal to 10.76 candela/m2 which is also equal to 10.76 lux.

    Physical Constants

    • Acceleration due to gravity: 32.2 ft/sec^2^ or 9.8 m/sec2.
    • Speed of light: 3.0 x 10^8^ m/sec.
    • Planck's constant: 6.626 x 10^‐34^ J‐sec.
    • Avogadro's number: 6.024 x 10^23^/ gram‐mole.

    Boolean Postulates

    • Boolean postulates are the basic laws of Boolean algebra, which is used to represent and manipulate logical expressions.

    Area Formulas

    • The area of a rectangle is found by multiplying its length and width.
    • The area of a square is found by squaring the length of its side.
    • The area of a triangle is found by multiplying its base and height and dividing the product by two.
    • The area of a circle is found by multiplying pi by the square of its radius.

    Volume Formulas

    • The volume of a rectangular solid or cuboid is found by multiplying its length, width, and height.
    • The volume of a cube is found by cubing the length of its edge or side.
    • The volume of a cylinder is found by multiplying pi, the square of the radius of the circular base, and the height.
    • The volume of a prism is found by multiplying the area of the base by the height.
    • The volume of a sphere is found by multiplying four-thirds pi, the cube of the radius of the sphere.
    • The volume of a pyramid is found by multiplying one-third, the area of the base, and the height of the pyramid.

    Trigonometric Functions

    • The Law of Cosines can be used to find the length of any side of a triangle if two sides and the angle between them are known: C^2^= a^2^ + b^2^ -- 2ab cos ^0^C
    • The Law of Sines can be used to find the missing side or angle of a triangle if you have the lengths of two sides and the measure of the angle opposite one of the sides: A/SinA=b/Sinb=c/Sinc

    Kinetic Energy

    • Kinetic Energy is the energy possessed by an object due to its motion.
    • It is calculated by multiplying half the mass of an object with the square of the velocity.
    • *KE = (1/2) * m * v^2^
    • The unit of kinetic energy is the Joule (J).

    Potential Energy

    • Potential Energy is the energy possessed by an object due to its position or state.
    • There are many forms of potential energy including gravitational potential energy, elastic potential energy, and chemical potential energy.
    • Potential energy is measured in Joules (J).

    Elastic Potential Energy

    • Elastic potential energy is the energy stored in an object due to its stretching or compressing.
    • For example, a stretched rubber band possesses elastic potential energy that can be released to perform work.
    • Hooke's Law states that elastic potential energy is directly proportional to the square of the amount of deformation.
    • If a spring is not stretched or compressed, then there is no elastic potential energy stored in it, and the spring is said to be at its equilibrium position.

    Force

    • A Newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s2 .
    • The unit of force is the Newton (N)
    • Force is a vector quantity, meaning it has both magnitude and direction.### Parameters
    • Describe the characteristics of a population.
    • Summarize data and represent the entire population.

    Null Hypothesis

    • States that there is no significant difference between populations.
    • Any observed difference is due to sampling or experimental error.
    • Represented as H0= M1=M2, indicating no difference between population means.
    • Used in conjunction with 95% confidence, implying a 95% chance of a true difference.

    Type I Error

    • Also known as False Positive or Alfa.
    • Occurs when the null hypothesis is rejected when it is true (should be accepted).
    • Indicates a difference between means when no actual difference exists.

    Type II Error

    • Also known as False Negative or Beta.
    • Occurs when the null hypothesis is accepted when it is false (should be rejected).
    • Indicates no difference in means when there is an actual difference.

    Coefficient of Variation (CV)

    • Also known as Relative Standard Deviation (RSD).
    • Measures the dispersion of a probability or frequency distribution.
    • Defined as the ratio of standard deviation (SD) to the mean.
    • Calculated as: S/Xmean = %

    Cumulative Error

    • Used to calculate the upper and lower confidence limits for air sampling.
    • Accounts for common errors like calibration, lab, instrument measurement, and correction errors during sampling and calculation.
    • As sample size increases, the result and assessment of mean are enhanced.

    Precision and Accuracy

    • Accuracy: How close a measurement is to the actual or accepted value. Assessed using F-test.
    • Precision: The value of standard deviation (SD) of repeated measurements of the same true or accepted value using the same measurement method.

    Lower Confidence Limit (LCL)

    • Used by OSHA officers to determine if a measured value exceeds the Permissible Exposure Limit (PEL).
    • If LCL > PEL, it indicates noncompliance.
    • If PEL > LCL, it indicates compliance.
    • Overexposure occurs when TWA or PEL >1 and LCL > PEL.

    Volume

    • 1 liter = 1000 cm3
    • 1 liter = 1000 ml
    • 1 m3 = 1000 liter
    • 1 liter = 1.06 qt = 61.02 in^3^ = 0.03531 ft^3^
    • 1 ml = 1 cm3
    • 1% by volume = 10,000 part per million (ppm)
    • 1,000,000/100=10,000
    • 1 ft^3^ = 7.5 gallons
    • 1 gallon of water = 8.34 lb
    • 1 gallon = 3.78 liters
    • 1 liter = 61.02 cu in
    • 1 hour = 3600 seconds

    Mass

    • 1 kg = 2.2 lb
    • 1 lb = 454 gram
    • 1 ton (US) =2000 lb

    Pressure

    • 1 atm = 14.7 psi = 760 mm Hg = 33.90 ft.

    Conversion Table

    Unit Conversion
    Pressure
    1 bar 14.5 PSI
    0.98 atm
    760 mm Hg
    10^5^ N/m^2^*
    *
    1 psia 51.72 mm Hg
    1 psig ADD 14.7 psia
    1 mm Hg 0.01934 psia
    Mass and Weight
    16 ounces 1 lb
    1 g 1000 mg
    2.205 lb 1kg
    1 ton 2000 lb
    1 tonne 1000 kg
    1 dram 1771.85 mg
    Heat Capacity
    1 bar 1 cal/g/°C
    = 1 Btu/lb/°F
    1 kN/m2 0.1450 psia
    Concentration
    1 bar 1 ppm = 1 mg/L
    1 kN/m2 0.009869 atm
    1 bar 1 mg/m3 = 1 × 10−9 g/cm3
    1 g/cm3 1 × 109 mg/m3
    Heat Capacity
    1 g/m3 62.42 lb/ft3
    1 Btu/lb/°F 1 cal/g/°C
    1 Btu/lb/°F 0.01602 g/cm3
    Force, Pressure, or Stress
    Pound-force 4.45 Newtons
    Pound-force/square inch 6.89 Kilopascals
    Illumination
    Foot-candle 10.76 lux
    Foot-lambert 3.426 Candela/square meter
    Length
    Inches 25.4 Millimeters
    Feet 0. 305 Meters
    Yards 0.914 Meters
    Miles 1 .61 Kilometers
    Area
    Square inches 645.2 Square millimeters
    Square feet 0.093 Square meters
    Square yards 0.836 Square meters
    Acres 0.405 Hectares
    Square miles 2.59 Square kilometers
    Volume
    Fluid ounce 29.57 Milliliters
    Gallons 3.785 Liters
    Cubic feet 0.028 Cubic meters
    Cubic yards 0.765 Cubic meters
    Mass
    Ounce 28.35 Grams
    Pounds 0.454 Kilograms
    Temperature
    Fahrenheit 5(°F − 32)/9 Celsius
    Celsius 9(°C + 32)/5 Fahrenheit
    Celsius °C + 273 Kelvin
    Fahrenheit °F + 460 Rankine

    Forces

    • Tension forces are forces that pull an object, opposite of compression forces.
    • Spring force is a force that is exerted by a compressed or stretched spring.

    Friction

    • Friction is a force that opposes motion between two surfaces in contact.
    • Frictional force is represented by F.
    • N is the force acting on the surface, in a direction perpendicular to the surface (normal force).
    • μ is the coefficient of friction, a dimensionless quantity that represents the roughness of the surfaces in contact.
    • F = μN is the equation for calculating frictional force.
    • When dealing with an angle, the equation becomes: *Nsin angle + μ N cos angle.

    Force and Distance

    • F1D1 = F2D2 expresses the relationship between force and distance. This principle is related to work and energy.

    Momentum

    • Momentum (often denoted by p) is a measure of the mass in motion.

    Velocity

    • v = v0 + at is the equation for velocity.
    • v is the final velocity.
    • vo is the initial velocity, where the acceleration is zero.
    • a is acceleration.
    • t is time.

    Distance

    • S = 𝐯𝟎𝐭 + ½ 𝐚𝐭^𝟐^, 𝐯^𝟐^ = 𝐯𝟎^𝟐^ + 𝟐𝐚𝐬 is a formula for calculating the displacement.
    • s is the distance travelled by the object in meters.
    • vo = the initial velocity, in meters per second.
    • a = the acceleration, in meters per second squared.
    • t = the time, in seconds.

    Work

    • W = FS, where W is work, in Joules (J).
    • F is force, in Newtons (N).
    • S is the distance moved against the force, in meters.

    Newton's Second Law

    • F = ma/g, where F is force in Newtons, m is mass in kilograms, a is acceleration in meters per second squared, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

    Example

    • A force acts on an object at a 30° angle, causing a displacement of 3 meters in the horizontal direction.

    Radiation Units

    • 1 rad = 10⁻² gray
    • 1 rem = 10⁻² sievert
    • 1 curie = 3.7 x 10¹⁰ becquerel
    • 1 becquerel = 1 disintegration/sec

    Density

    • Density of water = 1 gm/cm³ = 1.94 slugs/ft³ = 62.4 lb/ft³

    Light Units

    • 1 candela = 1 lumen/steradian
    • 1 footcandle = 10.76 candela/m² = 10.76 lux

    Physical Constants

    • Acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
    • Velocity of light = 3.0 x 10⁸ m/sec
    • Planck's constant = 6.626 x 10⁻³⁴ J‐sec
    • Avogadro's number = 6.024 x 10²³ / gram‐mole

    Area Formulas

    • Area of a rectangle = length × width
    • Area of a square = s², where s = side
    • Area of a triangle = (1/2) b × h, where b = base, h = height
    • Area of a circle = π × r², where r = radius

    Volume Formulas

    • Volume of a rectangular solid or cuboid = l × w × h, where l = length, w = width, h = height
    • Volume of a cube = a³, where a = length of edge or side
    • Volume of a cylinder = πr²h, where r = radius of the circular base, h = height
    • Volume of a prism = B × h, where B = area of the base, h = height
    • Volume of a sphere = (4/3)πr³, where r = radius of the sphere
    • Volume of a pyramid = (1/3) × B × h, where B = area of the base, h = height of the pyramid

    Trigonometric Functions

    • C² = a² + b² -- 2ab cos θC
    • A/SinA=b/Sinb=c/Sinc

    Kinetic Energy

    • KE is the energy of motion
    • KE = 1/2 mv², where m = mass, v = velocity

    Potential Energy

    • PE is stored energy
    • PE = mgh, where m = mass, g = acceleration due to gravity, h = height

    Elastic Potential Energy

    • Energy stored in elastic materials due to stretching or compression
    • Hooke's law explains that there is no elastic potential energy stored when a spring is not stretched or compressed.
    • The spring is said to be at its equilibrium position.

    Force

    • 1 newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s².

    Parameters

    • A parameter is a characteristic of a population.
    • They summarise data and the entire population.

    Null Hypothesis

    • There is no significant difference between the populations, if any observed difference is due to sampling or experimental error.
    • H0= M1=M2 means there is no difference between the populations.
    • Used in conjunction with 95% confidence, this means there is a 95% chance of the true population means being equal.

    Type I Error (False Positive-Alfa)

    • The null hypothesis is rejected when it is actually true.
    • This means you should accept the null hypothesis but reject it instead.
    • This indicates that there is a difference between the means, when there is no actual difference.

    Type II Error (False Negative-Beta)

    • The null hypothesis is not rejected when it is actually false.
    • This means you should reject the null hypothesis but accept it instead.
    • This indicates that there is no difference between the means, when there is actually a difference.

    Coefficient of Variation (CV)

    • Also known as the relative standard deviation (RSD).
    • A measure of the dispersion of a probability or frequency distribution.
    • It defines the ratio of the standard deviation to the mean.
    • CV = S/Xmean = %

    Cumulative Error

    • Used to calculate the upper and lower confidence limits for air sampling.
    • This is due to common errors: calibration, lab, instrument measurement, and correction errors during sampling and calculation.
    • As the sample size increases, the result and assessment of the mean is enhanced.

    Precision and Accuracy

    • Accuracy is how close a measurement is to the actual or accepted value.
    • Precision is the value of the standard deviation of repeated measurements of the same true value.
    • Both precision and accuracy are important in industrial hygiene.
    • F-test can be used for accuracy evaluation.

    Lower Confidence Limit (LCL)

    • Used by OSHA to determine if the measured value exceeds the Permissible Exposure Limit (PEL).
    • If LCL > PEL, then it is a noncompliance with the OSHA standard.
    • If PEL > LCL then it is a compliance.
    • Overexposure occurs when TWA or PEL >1 and LCL > PEL.
    • LCL must be less than the PEL for compliance with OSHA standards.

    Volume

    • 1 liter = 1000 cm3
    • 1 liter = 1000 ml
    • 1 m3 = 1000 liter
    • 1 liter = 1.06 qt = 61.02 in^3^ = 0.03531 ft^3^
    • 1 ml = 1 cm3
    • 1% by volume = 10,000 part per million (ppm) 1,000,000/100=10,000
    • 1 ft^3^ = 7.5 gallons
    • 1 gallon of water = 8.34 lb
    • 1 gallon = 3.78 liters
    • 1 liter = 61.02 cu in
    • 1 hour = 3600 seconds

    Mass

    • 1 kg = 2.2 lb
    • 1 lb = 454 gram
    • 1 ton (US) =2000 lb

    Pressure

    • 1 atm = 14.7 psi = 760 mm Hg = 33.90 ft.

    Conversions

    • 1 bar = 100 kPa = 14.5 PSI = 0.98 atm = 760 mm Hg
    • 1 psia = 51.72 mm Hg
    • 1 psig = 14.7 psia
    • 1 mm Hg = 0.01934 psia

    Mass and Weight

    • 16 ounces (oz) = 1 lb
    • 1 g = 1000 mg
    • 2.205 lb = 1kg
    • 1 ton (US) = 2000 lb
    • 1 tonne (Metric ton) = 1000 kg
    • 1 dram = 1771.85 mg
    • 1 bar = 100 cal/g/°C = 1 Btu/lb/°F
    • 1 kN/m2 = 0.1450 psia
    • 1 bar = 1 ppm = 1 mg/L
    • 1 kN/m2 = 0.00986 9 atm
    • 1 bar = 1 mg/m3 = 1 × 10−9 g/cm3
    • 1 g/cm3 = 1 × 109 mg/m3
    • 1 g/m3 = 62.42 lb/ft3
    • 1 Btu/lb/°F = 1 cal/g/°C
    • 1 Btu/lb/°F = 0.01602 g/cm3
    Force, Pressure, or Stress
    • 1 Pound-force = 4.45 Newtons
    • 1 Pound-force/sq inch = 6.89 Kilopascals

    Illumination

    • 1 Foot-candle = 10.76 Lux
    • 1 Foot-lambert = 3.426 Candela/square meter
    • 1 tesla = 10,000 gauss
    • 1 becquerel = 1 disintegration/s

    Forces

    • Tension forces pull an object, the opposite of compression.
    • Spring force is exerted by a compressed or stretched spring.

    Friction

    • Friction force opposes motion or prevents relative motion between systems in contact.
    • Force, acting on the surface, is normal (perpendicular).
    • 1 Newton (N) = 1 Kg*m/s2 and 1 kg = 2.2 lbs.
    • To calculate the force of friction:
      • Multiply the coefficient of friction (μ) by the normal force (N).
      • F = μN
      • If there is an angle, use *Nsin angle + μ N cos angle.

    Force and Distance

    • The product of a force and the distance it acts over is a constant.
    • F1D1 = F2D2

    Momentum

    • The product of an object's mass and velocity.

    Velocity

    • **v = v0 + at **
    • v = final velocity, in meters per second (m/s)
    • vo = original velocity at the start of the acceleration, in m/s
    • a = acceleration, in m/s2
    • t = time in seconds

    Distance

    • S = 𝐯𝟎𝐭 + ½ 𝐚𝐭^𝟐^, 𝐯^𝟐^ =𝐯𝟎^𝟐^ + 𝟐𝐚𝐬
    • s = distance from its original position, in meters
    • vo = initial velocity before the start of the acceleration, in m/s
    • a = acceleration, in m/s^2
    • t = time, in seconds

    Work Done

    • W = FS
    • W = work done, in Joules (J)
    • F = force, in Newtons (N)
    • S = distance from its original position, in meters

    Newton's Second Law

    • F = ma/g
    • m = mass
    • a = acceleration
    • g = 9.8 m/s^2 or 32.2 ft/s^2 (US units)

    Radiation Units

    • 1 rad = 10-2 gray
    • 1 rem = 10-2 sievert
    • 1 curie = 3.7 x 1010 becquerel
    • 1 becquerel = 1 disintegration/sec

    Density of Water

    • 1 gm/cm3 = 1.94 slugs/ft3
    • Weight density = 62.4 lb/ft3

    Light

    • 1 candela = 1 lumen/steradian
    • 1 footcandle = 10.76 candela/m2 = 10.76 lux

    Physical Constants

    • Acceleration of gravity: 32.2 ft/sec2 = 9.8 m/sec2
    • Velocity of light: 3.0 x 108 m/sec
    • Planck’s constant: 6.626 x 10-34 J-sec
    • Avogadro’s number: 6.024 x 1023/gram-mole

    Area

    • Rectangle: Area = length x width
    • Square: Area = s2, where s = side
    • Triangle: Area = (1/2) b x h, where b = base and h = height
    • Circle: Area = π x r2, where r = radius

    Volume

    • Rectangle Solid/Cuboid: V = l × w × h, where l = Length, w = Width, h = Height
    • Cube: V = a3 where a = Length of edge or side
    • Cylinder: V = πr2h where r = Radius of the circular base, h = Height
    • Prism: V = B × h, where B = Area of base, h = Height
    • Sphere: V = (4⁄3)πr3 where r = Radius of the sphere
    • Pyramid: V = (1⁄3) × B × h, where B = Area of the base, h = Height

    Trigonometric Functions

    • Right Triangle Definitions for Trigonometry Functions
    • C2 = a2 + b2 - 2ab cos0C
    • A/SinA = b/Sinb = c/Sinc

    Kinetic Energy

    • v = the object's speed (velocity)

    Potential Energy

    • Potential energy refers to the energy possessed by an object due to its position or configuration. It is a form of stored energy that can be converted into kinetic energy.

    Elastic Potential Energy

    • Energy stored in elastic materials due to stretching or compressing.
    • Hooke’s Law states that no elastic potential energy is stored in a spring if it is not stretched or compressed.
    • The spring is said to be at its equilibrium position when it's neither stretched nor compressed.

    Force

    • A newton (N) is the amount of force required to accelerate a 1-kg mass by 1 m/s2

    Parameters

    • Parameters are used to describe characteristics of a population.
    • They summarize data and represent the entire population.

    Null Hypothesis

    • The null hypothesis states that there is no significant difference between the populations.
    • Any observed differences are due to sampling or experimental error.
    • It is often stated as H0=M1=M2, meaning there is no difference between the population means.
    • It is used in conjunction with a 95% confidence level, which means there is a 95% chance the null hypothesis is true.

    Type I Error

    • Type I error (false positive, denoted as "α") occurs when you reject the null hypothesis when it's actually true.
    • You conclude there is difference between the means when there is actually no difference.

    Type II Error

    • Type II error (false negative, denoted as "β") occurs when you fail to reject (accept) the null hypothesis when it's actually false.
    • You conclude there is no difference between the means when there is actually a difference.

    Coefficient of Variation (CV)

    • The coefficient of variation (CV) is a measure of the dispersion of a probability distribution or frequency distribution.
    • It represents the ratio of the standard deviation (SD) to the mean (X̄) and is often expressed as a percentage: CV = (SD / X̄) × 100%.

    Cumulative Error

    • Cumulative error is used to calculate the upper confidence limit (UCL) and lower confidence limit (LCL) for air sampling.
    • It accounts for common errors such as calibration, lab, instrument measurement, and correction errors during sampling calculations.
    • As sample size increases, the result and assessment of the mean are enhanced.

    Precision and Accuracy

    • Accuracy refers to how close a measurement is to the actual or accepted value.
    • Precision refers to the variability of repeated measurements of the same true or accepted value using the same measurement method. It is often represented by the standard deviation (SD).

    Lower Confidence Limit (LCL)

    • The LCL is used by OSHA officials to determine if a measured value exceeds the Permissible Exposure Limit (PEL).
    • If the LCL is greater than the PEL, there is noncompliance with regulations.
    • If the PEL is greater than the LCL, there is compliance with regulations.

    Conversion Factors

    • 1 bar = 100 kN/m2 = 1 atm = 14.5 psi = 0.98 atm = 760 mm Hg = 105 N/m2
    • 1 psia = 51.72 mm Hg
    • 1 psig = 14.7 psia
    • 1 mm Hg (Torr) = 0.01934 psia
    • 16 ounces (oz) = 1 lb
    • 1 g = 1000 mg
    • 2.205 lb = 1 kg
    • 1 ton (US) = 2000 lb
    • 1 tonne (Metric ton) = 1000 kg
    • 1 dram = 1771.85 mg
    • 1 bar = 100 cal/g/°C = 1 Btu/lb/°F
    • 1 kN/m2 = 0.1450 psia
    • 1 bar = 1 ppm = 1 mg/L
    • 1 kN/m2 = 0.009869 atm
    • 1 bar = 1 mg/m3 = 1 × 10−9 g/cm3
    • 1 g/cm3 = 1 × 109 mg/m3
    • 1 g/m3 = 62.42 lb/ft3
    • 1 Btu/lb/°F = 1 cal/g/°C
    • 1 Btu/lb/°F = 0.01602 g/cm3
    • 1 pound-force = 4.45 newtons
    • 1 pound-force/square inch = 6.89 kilopascals
    • 1 foot-candle = 10.76 lux
    • 1 foot-lambert = 3.426 candela/square meter

    Units

    • 1 liter = 1000 cm3 = 1000 ml
    • 1 m3 = 1000 liter
    • 1 liter = 1.06 qt = 61.02 in^3 = 0.03531 ft^3
    • 1 ml = 1 cm3
    • 1% by volume = 10,000 part per million (ppm)
    • 1 ft^3 = 7.5 gallons
    • 1 gallon of water = 8.34 lb
    • 1 gallon = 3.78 liters
    • 1 liter = 61.02 cu in
    • 1 hour = 3600 seconds

    Mass

    • 1 kg = 2.2 lb
    • 1 lb = 454 gram
    • 1 ton (US) =2000 lb

    Pressure

    • 1 atm = 14.7 psi = 760 mm Hg = 33.90 ft.

    Tension Forces

    • Tension forces are required to pull an object, the opposite of compression.
    • Examples of tension forces include pulling a rope, stretching a rubber band, or lifting a weight.

    Spring Force

    • A spring, when compressed or stretched, exerts a spring force.
    • The force the spring exerts is proportional to how much it is stretched or compressed.

    Frictional Force

    • Frictional force is the force that opposes motion between two surfaces in contact.
    • It acts in the direction opposite to the motion of the object.
    • The frictional force is proportional to the normal force, represented by N, which is the force acting on the surface perpendicular to the surface.
    • The coefficient of friction, denoted by μ, is a constant that represents the ratio of the frictional force and the normal force.
    • To calculate frictional force, use the formula F= μN.
    • If the object is on an inclined surface with an angle, then the formula for calculating the frictional force becomes: Nsin angle + μ*N cos angle.
    • The unit of measurement for force is Newton (N), which is equal to 1 kilogram-meter per second squared (kg*m/s^2).
    • 1 kilogram is equal to 2.2 pounds.

    Force and Distance

    • The relationship between force and distance is expressed as F1D1 = F2D2.
    • This equation implies that if the force is doubled, the distance traveled is halved, and vice-versa.

    Momentum

    • Momentum is a measure of the mass and velocity of an object.
    • It is calculated as the product of mass and velocity.

    Velocity

    • Velocity is the measure of how fast an object is moving and in what direction.
    • It is calculated using the formula v = v0 + at, where:
      • v represents the final velocity (meters per second).
      • v0 represents the initial velocity at the start of the acceleration (meters per second).
      • a represents the acceleration (meters per second squared).
      • t represents the time (seconds).

    Displacement and Velocity

    • The following equations are used to calculate displacement and velocity:
      • S = 𝐯𝟎𝐭 + ½ 𝐚𝐭^𝟐^, which represents the displacement from the original position (meters).
      • 𝐯^𝟐^ = 𝐯𝟎^𝟐^ + 𝟐𝐚𝐬, which represents the final velocity (meters per second).
    • s is the distance from the object's original position (meters)
    • vo is the initial velocity before the acceleration (meters per second)
    • a is the acceleration (meters per second squared)
    • t is the time (seconds).

    Work Done

    • Work done is the amount of energy transferred by a force acting over a certain distance.
    • It is calculated using the formula W = FS, where:
      • W represents the work done (Joules).
      • F represents the force (Newton).
      • S represents the distance from its original position (meters).

    Newton's Second Law of Motion

    • Newton's second law states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma/g), where:
      • F represents the force (Newton).
      • m represents the mass (kilograms).
      • a represents the acceleration (meters per second squared).
      • g represents the acceleration due to gravity which is 9.8 m/s^2 or 32.2 ft/s^2.

    Force Acting at an Angle

    • If a force acts at an angle to the horizontal, the horizontal component of the force is responsible for the horizontal displacement of the object.
    • The horizontal component of the force can be calculated using the formula F*cos θ, where θ is the angle between the force and the horizontal direction.
    • This information helps determine the work done by the force in the horizontal direction.

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