Physical Quantities and Units

Physical Quantities and Units

• Physical quantities and units relate to measurement.
• Measuring involves being able to count the numbers of particular items.
• It is possible to count how many times a physical quantity is greater or less in one case compared to another.
• It is important to have a complete specification for the method of counting.

How Units are Defined

• A unit requires a special name and symbol.
• The usefulness of a unit is to act as a means of communicating to everyone doing science.
• Making a desk involves defining length, breath, and height.
• Dimensions are determined as ratios compared to defined units.
• Numerical magnitude is displayed via units.
• Defined units must be unambiguously defined, reproducible to a great accuracy, and accepted by most people.

SI Units

• SI units, adopted in 1960, represent a set of basic physical quantities.
• A second is defined as a number of periods of radiation from the cesium-133 atom.
• A metre is the distance travelled by light in a vacuum during 1/299 792 458 of a second.
• A kilogram is the mass of a specific platinum alloy cylinder kept at the International Bureau of Weights in France.
• A kelvin is 1/273.16 of the thermodynamic temperature of the triple point of water.
• An ampere is the constant current maintained in two straight parallel conductors of infinite length and negligible cross section, placed one metre apart in a vacuum which would provide a force equal to 2 x 10^-7 newtons per metre of length between the conductors.
• A mole is the amount of substance containing as many elementary entities as there are atoms in 12 grams of carbon-12.

Magnitudes & Metric System Prefixes

• Exa (E) represents 1,000,000,000,000,000,000 (10^18).
• Peta (P) represents 1,000,000,000,000,000 (10^15).
• Tera (T) represents 1,000,000,000,000 (10^12).
• Giga (G) represents 1,000,000,000 (10^9).
• Mega (M) represents 1,000,000 (10^6).
• Kilo (k) represents 1,000 (10^3).
• Hecto (h) represents 100 (10^2).
• Deka (da) represents 10 (10^1).
• Deci (d) represents 0.1 (10^-1).
• Centi (c) represents 0.01 (10^-2).
• Milli (m) represents 0.001 (10^-3).
• Micro (m) represents 0.000 001 (10^-6).
• Nano (n) represents 0.000 000 001 (10^-9).
• Pico (p) represents 0.000 000 000 001 (10^-12).
• Femto (f) represents 0.000 000 000 000 001 (10^-15).
• Atto (a) represents 0.000 000 000 000 000 001 (10^-18).

Scalars and Vectors

• Scalars are quantities that are fully described by magnitude alone, like SI base units.
• Vectors are quantities that are fully described by both magnitude and direction.

Fundamental Quantities

• A fundamental quantity is an independent physical quantity that cannot be expressed in terms of other physical quantities.
• Fundamental quantities are used as the basis for derived quantities.
• Length, mass, time, electric current, and thermodynamic temperature are all examples of fundamental quantities in physics.
• Various units are associated with base quantities. Length (metre, M) has units; Centimeter (m), millimeter (mm), kilometer (km).
• Mass (kilogramme, Kg) has units of gramme (g).
• Time (second, S) has units of minute (min) and hour (h).
• Temperature (Kelvin, K) has Celsius (°C) and Fahrenheit (°F) units.
• Current (Ampere, A) has milliampere (mA) and microampere (µA) units.
• Amount of substance in Mole (Mol) and luminous intensity in candela (cd)

Derived Quantities

• Derived quantities are physical quantities calculated from two or more fundamental quantities, and cannot be measured directly but computed.
• Many derived quantities are calculated in physics; area, volume, and density are three examples.
• Area (Length x breadth) is measured in square metres (m^2).
• Volume (Length x breadth x height) is measured in cubic metres (m^3).
• Density (Mass / volume) is measured in kilograms per cubic metre (kg/m^3).
• Speed or velocity (Distance / time) is measured in metres per second (m/s).
• Acceleration (Change in velocity / time) is measured in metres per second squared (m/s^2).
• Force momentum (Mass x acceleration due to gravity) is measured in newtons (N)
• Pressure (Force / area) is measured in pascals (Pa).
• Energy or work (Force x distance) is measured in joules (J), which is equal to Nm.
• Power (Work / time) is measured in watts (W), which is equal to Nm/s.
• Electric potential is measured in volts (V), which is equal to Kgm²/AS³ or Kgm^2S^-3A^-1

Quantities and Their Measuring Instruments

• Mass is measured using beam balances, chemical balances, or electronic balances.
• Length is measured using metre rules, Vernier calipers, pairs of calipers, surveyors' tapes, or measuring tapes.
• Volume is measured using graduated beakers, volumetric flasks, measuring cylinders, or burette pipettes.
• Time is measured using stop watches, stop clocks, or electronic watches/clocks.
• Temperature is measured using absolute or clinical thermometers.
• Atmospheric pressure is measured using fortins or aneroid barometers.
• Electric potential is measured using voltmeters.
• Electric current is measured using ammeters.
• Luminous intensity is measured using photometers.

Regular and Irregular Objects

• Regular objects are objects with fixed shapes and dimensions.
• Irregular objects are objects that do not have fixed shapes or dimensions.

Regular Volume Object

• Solids of regular shapes have regular volumes
• Volumes of regular solids are acquired by measuring and calculating by formulae
• For example a solid of 8cm length, 4cm breadth and 1cm height, its volume is calculated; length x breadth x height = 8cm x 4cm x

Irregular Volume Object

• In cases where the volume of the abject to be measure of regular volume, the volumes of liquids and other irregular volumes can be measured by;
• Special measuring containers like graduated measuring cylinders, volumetric and burette, and pipettes.
• General precautions when measuring volumes:
  • The cylinder (or any other container) should be washed with water and with a small amount of the liquid to be measured first
  • The cylinder should be placed on a horizontal plane.
  • When measuring the liquid's dimensions, the eye position must be in line to the surface of the liquid.

Finding Volume of Objects that sink in water using a Measuring cylinder

• Take some water into a measuring cylinder and note the measurement
• Slowly lower an solid into the water until it is completely inmersed
• The water level will rise, giving the volume of the water and submerged sold
• The second volume minus the first volume gives the volume of the solid.
• Volume of water = Wcm³; Volume of water + submerged solid = Scm³; Therefore, volume of solid = (S – W) cm³

Using an Overflow Can

• Pour water into an overflow can until some of it flows out.
• Measuring Cylinder is used to measure
• Place a Measuring Cylinder under the outlet
• Then Lower solid into the Over Flow Can, displacing the water from the can into cylinder, the volume water displaced is equivalent to the volume of the solid.
• volume of displaced water from the measuring cyllinder provides the volume of the submerged solid.

Finding Volume of Objects that sink using measuring cylinder

• Measure the volume of Substances with Irregular shapes , such as cork and wood
• Cork and wood don't sink/float in water
• Thus additional solid has to be tied to wood/Cork for Irregular shapes with floating substances, like steal, stopper e.tc
• The stopper along with cork/wood now makes the entire assembly now sink; these solids are know as sinkers
• For example;
  • Measure the water with measuring cyllinder
  • Tie the steal/stopper as singers
  • Gen stopper into the water and note the volume of the water
  • Take out the glass stopper and tie it to the cork stopper and the cork into the water and note the volum
  • volume of water + sinker = S cm³; Volume of water + sinker + cork = C cm³; Therefore, volume of cork = (C – S) cm³

Teaching of Force

• The concept of force is a push or pull.
• When there is interaction between two objects, there is a force upon each of the objects. When interaction ceases, the two objects no longer experience the force.
• Forces only exist as a result of an interaction.
• A force is a push or pull upon an object resulting from that object's interaction with another object.
• Force is a quantity that is measured using the metric unit known as the Newton.
• A Newton is abbreviated by "N", and one Newton is the amount of force required to give a 1 kg mass an acceleration of 1 m/s/s.
• 1 Newton = 1 kg * m/s^2
• Push force is that which makes an object starts from what was the state of rest
  • Example, pushing trolley, car or table
• Pull force is that which pulls resulting in change in position
  • Example pulling curtain, dragging a box, opening a door
• Two types of forces exist.
  • Contact force; frictional, tension normal etc,
  • Non contact force, or "action at a distance", gravitational, electric, magnetic , nuclear force etc.
• Contact forces occur when the two interacting objects physically contact each other; frictional, tensional, normal, air resistance, appplied, and spring forces
• Non-contact distances occur even if the object exerting a push or pull is not in physical seperations
  • Gravitational force; the sun and planets exert that at large seperations
  • Electrical forces: an example are atomic nucleuses causing a pull towards each other despite small size
  • Magnetic forces occurs even when there is distance between the objects within a few centimeters
• Types of Non contact force; gravitational, elctric, magnetic, nuclear force