Physics Notes PDF: SI Units, Forces, Energy, and Motion

Okay, here's the conversion of the images into a structured markdown format. I've done my best to transcribe the text, format it, and describe any visual elements. # PHYSICS ## SI Units * There are 7 basic quantities and units: * Electrical Current - Amperes (A) * Luminous Intensit...

Okay, here's the conversion of the images into a structured markdown format. I've done my best to transcribe the text, format it, and describe any visual elements. # PHYSICS ## SI Units * There are 7 basic quantities and units: * Electrical Current - Amperes (A) * Luminous Intensity - Candela (cd) * Temperature - Kelvin (K) * Mass - Kilogram (Kg) * Length - Metre (m) * Amount - Mole (mol) * Time - Second (s) * Prefixes used for scalar & vector quantities: * kilo: $10^3$ (K) * Deci: $10^1$ (d) * Centi: $10^{-2}$ (c) * Milli: $10^{-3}$ (m) * Micro: $10^{-6}$ (N) * Nano: $10^{-1}$ (n) ## FORCES & ENERGY * A force is simply an agent that produces or tends to produce motion and/or rest. * Speed is the distance moved in a given period of time. Speed can be found using: $average\ speed = \frac{distance\ moved}{time\ taken}$ * Speed is a scalar quantity (has only magnitude). Velocity is speed in a certain direction, making it a vector quantity. Velocity can be found using: $velocity = \frac{displacement}{time}$ * Alternatively, a vector quantity has both magnitude and direction. * Acceleration is the measure of the rate of increase in velocity. It is also a vector quantity. Acceleration can be found using: $acceleration = \frac{increase\ in\ velocity}{time\ taken}$ * Deceleration, or Retardation, is the rate of decrease in velocity * If an object decelerates at $3 m/s^2$ its acceleration is $-3 m/s^2$. * Although $m/s^2$ is acceptable, the unit $ms^{-1}$ is more commonly accepted. $\frac{m}{s^2} = ms^{-1}$ * A distance-time graph is plotted to show the increase in distance over time. * The graph shows distance on the y-axis and time (independent) on the x-axis. * The graph is a curve that starts shallow and gets steeper, indicating acceleration. * The graph is labeled with the following: Distance-Time graph for an accelerating car. * The gradient of the distance-time graph shows the velocity of the car. This can be found using: $Gradient = \frac{y_2 - y_1}{x_2 - x_1}$ * A velocity-time graph shows the changing velocity over time. * The graph shows velocity on the y-axis and Time (independent) on the x-axis. * The graph shows a stepped line where there is a period of 0 velocity, then constant, and then a period of acceleration. * The graph is labeled with the following: Velocity-Time graph of a moving car * The gradient of a velocity-time graph is the acceleration of that specific object (same formula). * The area under a velocity-time graph is the distance that object has moved. * There are 3 main equations of motion. These are: 1. $v = u + at$ 2. $S = ut + \frac{1}{2} at^2$ 3. $v^2 = u^2 + 2as$ Where: * v = final velocity * u = initial velocity * s = distance * t = time * a = acceleration * While they may be used interchangeably, Mass and Weight are completely different things. The differences are: | Mass | Weight | | ----------------------------- | ---------------------------------- | | The amount of matter present in a body. | The force exerted on the ground. | | Unit => Kg (Kilograms) | Unit => N (Newtons) | | Independent of weight. | Dependent on mass | | Remains constant accross different gravitational strengths. | Changes across different gravitational strengths. | | Formula: None | Formula: W=mg (g = gravitational strength) | | Scalar quantity | Vector quantity | | Independent of gravity | Dependent on gravity | | Has no given direction | Has given direction (downwards) | * The gravitational strength of Earth is almost constant 9.8 $m/s^2$ or $ms^{-1}$. However, it should be noted that in the cases of free fall, $a(acceleration) = g$. * Common Example: * A vertical diagram shows a person dropping a ball from a building. * The initial velocity (v) is 0. * The ball accelerates downwards, indicated by multiple arrows. * The final velocity is labeled as $v_{(final \ velocity)}$ * acceleration (a) or $g = 9.8 \ ms^{-1}$ * A person on a building drops a ball (not throwing with force) * However, it should be noted that an object only accelerates until it reaches its terminal velocity. Terminal velocity is the highest attainable velocity of an object while falling through mid-air. It can be found using: $V = \sqrt{\frac{3mg}{pAC}}$ where: * v = terminal velocity * m = mass of falling object * g = gravitational acceleration * p = density of fluid through which the object is falling * A = the projected area of the object * C = the drag coefficient * The value of g varies slightly from place to place on Earth, but is roughly $\approx 9.8 \ ms^{-1}$. * Gravity pulls all objects towards the earth at the same time naturally. However, some light objects fall slower due to air resistance. This is why all objects would fall together in a vacuum. * Force, mass and acceleration are all relatable. Issac Newton's 3 laws of motion best describes them. * Newton's Laws of motion: 1. Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it. 2. Force is equal to the change, in Momentum per change in time. For a constant mass, force equals mass times acceleration. 3. For every action, there is an equal and opposite reaction. * The first law of motion explains how everything has inertia to change in State of motion or rest. It will remain Stationary or moving unless external forces act upon it. * The second law can be summarized: $Force = mass \times acceleration (F = ma)$, or can be replaced by $Weight = mass \times gravitational \ strength (w = mg)$ * The third law of motion explains how the net result of every force is 0, due to an equal but opposite reaction. * How force/weight changes from Earth to moon ($f=w$, $g=a$) * Diagram showing Earth and the Moon. On the earth there is $m = 1 kg$, and $g= 9.8$, so $W=9.8N$. * On the moon there is $m = 1 kg$, and $g= 1.6$, so $W=1.6N$. * Mass is constant, while weight changes * when materials try to slide across each other, a force called friction stops them. The types of friction are: * Static: The friction between objects that start to slide. * Dynamic: The friction during the sliding. * Fluid: The friction caused when an object tries to slide inside a gas or a liquid. * There are several types of motion: * Straight-line motion * Projectile motion * Centripetal motion * Diagram shows an object moving in a circle. $like \ y= x^2?$ * Centripetal motion is circular motion produced by forces applied at right-angles. This can be found by: $Centripetal \ force = \frac{mv^2}{r} \ rasius \ of \ circle$ * Immediately after centripetal force, if the wire or what is causing right-angular motion stops doing so, the object will travel straight on due to centrifugal force. * Diagram shows the path of circular motion, and where, if the centripetal froce stopped, the object would "snap" off along the tangent. * The earth's gravity also causes objects such as satelites to travel in centripetal motion. To escape this, the object must reach escape velocity, which is 11,000 m/s. * The momentum of an object is its mass x velocity. It is the "quantity" of motion in a moving body: 1. Momentum = mass x velocity 2. $Force =\frac{mv - mu}{t}$, where * mv is the final momentum * mu is the initial momentum * So Force = rate of change of momentum * This formula can be rearranged to say: $F_t = mv - mu$ * Impulse == Gain in momentum * Impulse is really just the change in momentum * Momentum is conserved when two objects collide. Their sum remains the Same: * This can be given from the formula $ (m_1 \times u_1) + (m_2 \times u_2) = m_1v + m_2v$ * V is constant as the final velocity will remain the same. * All this confirms Newton's 2nd Law * Finding resultant forces between objects directly horizontal or vertical is simple addition/subtraction. These are shown as block and arrow diagrams. * The resultant forces of angular forces is found by the Parallelogram rule: * A diagram showing addition of forces using vectors to find the resultant. It shows an a force of 25 N. acting on the right angle to a force of 43 N. The resultant force has a magnitude if 50 N. * Two forces can also be acting on the same object. If the object is Straight, it is in a state of equilibrium, where the clockwise and anti-clockwise moments are equal. A moment of a force is a measure of the turning effect of the force about a particular point. It is found by: $Moment = force \times distance, \ Units (Nm) = (N) \times (m)$ * For equilibrium, the sum of forces in one direction must equal those of the other direction. Plus, the principle of moments must apply. * Using the principle/concept of moments, couples are created? These are long, parallel yet opposite forces...? A force of 6N acting at a distance of 4m, gives an resulting moment of $6 \times 4 = 24 Nm$ * The moment amount of a couple is called its torque. * Considering the rules for equilibrium, there are different forms of stability. These are dependent upon: * Center of gravity: Where the weight of an object pulls. * Center of mass: The mean position of the mass of an object. * There are 3 types of equilibrium: *Stable*, *Unstable*, *Neutral* * stable * the center of gravity has space besides it * unstable * the center of gravity has less space besides it * neutral * the center of gravity stays the same * Work (in Physics) is done when a force produces movement. The SI unit for work is Joule. It can be found by: $W = fs$ Weight$\rightarrow$ Force $\leftarrow$Distance * To work, everything needs energy. There are different types of these: * Thermal Heat * Kinetic: Moving * Potential: stored * Electrical: Relating to current * Chemical: Relating to chemicals * Kinetic energy is created when particles collide with one another, causing effective collision. This process can be sped up by providing more heat to the particles, and reducing their masses, Kinetic * Energy can be determined using the formula: $Kinetic \ Energy = \frac{1}{2} m v^2$ * Potential energy is the stored, energy, and is found by: $Potential \ Energy = mgh$ * Energy cannot be created or destroyed, it only converts into other forms. After the work is done, the energy is subsequently transferred. * The energy crisis has taken a step forward in the whole world, for which, new methods have to be come up with. But they are releasing carbon dioxide and causing Climate Change (see IDU topic). * The power of any energy source is the rate at which it gets work done. It can be measured by: $Power = \frac{work \ done}{time} = \frac{energy \ transformed}{time}$ * It is measured by watts (w) * In motion examples, it is true that: $Power = force \times velocity$ * The efficiency of an energy source Is hence also measured by: $Efficiency = \frac{power \ output}{power \ input}$ * In Physics, density refers to the degree of compactness of a substance. Pure water has a density of 1.00. Density is given by: $\rho = \frac{m}{v}$ * m = mass * v volume * $\rho$ density * To find the relative density of a fluid (relative density is how many more times dense a fluid is compared to water), the following two formulae are used: $relative \ density = \frac{density \ of \ substance}{density \ of \ water}$ $relative \ density = \frac{mass \ of \ substance}{mass \ of \ some \ volume \ of \ water}$ * Unlike density, Pressure refers to the constant physical force exerted on an object by something in contact with it. * Measured in Pascals (Pa). $1Nm^{-1} = 1 Pa.$ * Pressure is defined by: $P = \frac{f}{A} \ \ Force$ $\ \ Area$ * Waves * Waves are mediums of transferring energy without particles. In layman's terms, they are disturbances propagating through space. * Two types of waves: * Longitudinal (coils move horizontally) * Transverse (coils move vertically) * Longitudinal Wave * Transverse wave: *Diagram showing parts of a wave: crest, wavelength, amplitude and trough.* * The wavelength is the distance from ore point to the same in the next oscillation.(Length of an oscillation) - $\lambda$ * The amplitude is the distance from the maximum $\rightleftharpoons$ minimum point to the mean line. * The time period of a wave is the time taken for an oscillation. The frequency (Hz) is the number of oscillations in one second. They are inversely proportional. $ T = \frac{1}{f}; \ \ \ f = \frac{1}{T}$