MEASUREMENT OF PHYSICAL QUANTITIES (MASS, WEIGHT, TIME, ELECTRIC CURRENT Lesson Note
This SS1 Physics lesson note covers MEASUREMENT OF PHYSICAL QUANTITIES (MASS, WEIGHT, TIME, ELECTRIC CURRENT for First Term, Week 2.
Learning Objectives
- By the end of the lesson, students should be able to:
- 1. Define physical quantities
- 2. Distinguish between fundamental and derived quantities
- 3. State the SI units of length, mass, time and electric current
- 4. Differentiate between mass and weight
- 5. Explain dimensional analysis and its uses
Lesson Note
MEASUREMENT OF PHYSICAL QUANTITIES
A. INTROUCTION:
In physics, anything you can measure with an instrument and give a numerical value and a unit is a physical quantity.
Example: If you measure your height, you will get a number e.g 1.6 and a unit e.g metres. So 1.6m is a physical quantity. But love, truth and kindness cannot be measured with any instrument- so they are not physical quantities.
B. PHYSICAL QUANTITIES
A physical quantity is any quantity that can be measured. Examples are length, mass, time, etc.
TYPES OF PHYSICAL QUANTITIES
a. Fundamental Quantities: These are basic quantity that are independent upon which the unit of other quantities depend. These are length, mass, and time.
NB: In most scientific measurement, the system of unit now accepted internationally is called System International of Unit (S.I)
FUNDAMENTAL QUANTITIES AND S.I UNIT
| QUANITY | S.I UNIT | UNIT ABBREVIATION |
|---|---|---|
| Length | Metre | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Temperature | Kelvin | K |
| Electric current | Ampere | A |
| Amount of substance | Mole | Mol |
| Luminous intensity | Candela | cd |
C. INSTRUMENT FOR MEASUREMET
1. LENGTH
Length is the distance between two points. SI Unit is metre (m).
i. Metre rule / Half-metre rule: For short lengths e.g. length of book, height of table. Measures in cm and mm.
ii. Tape rule / Measuring tape: For longer lengths e.g. height of classroom, length of field, tailor uses it.
iii. Vernier Caliper: For very small lengths, diameter of wire, inside diameter of pipe. Measures to 0.01cm (0.1mm). Used in workshop.
iv. Micrometer Screw Gauge: For even smaller thickness e.g. thickness of paper, diameter of thin wire. Measures to 0.001cm (0.01mm).
2. MASS
Mass is the quantity of matter in a body. SI Unit is kilogram (kg). Note: Mass is NOT weight.
Beam Balance / Lever Balance: Compares mass of object with standard masses. Used in laboratory and market. Types: equal arm, triple beam.
Chemical / Electronic Balance: For very small mass in laboratory e.g. 0.001g. Used in Chemistry lab.
Spring Balance: Actually measures weight, but can be calibrated to mass. Measures in kg or N.
iv. Bathroom Scale / Weighing Scale: For body mass.
3. TIME
Time is the interval between two events. SI Unit is second (s).
i. Clock: For measuring time in hours, minutes, seconds. Wall clock, wristwatch.
ii. Stopwatch / Stop clock: For short time intervals e.g. time for 100m race, period of pendulum. Digital stopwatch is more accurate to 0.01s.
iii. Pendulum / Heartbeat: In olden days, before clocks.
iv. Atomic Clock: Most accurate, used in laboratories and for satellite timing.
4. ELECTRIC CURRENT
Electric current is the flow of electric charges. SI Unit is Ampere (A).
i. Ammeter: Connected in series in a circuit to measure current.
ii. Milliammeter - measures small current in milliampere (mA)
iii. Microammeter - measures in microampere (µA)
iv. Galvanometer: Detects very tiny current and direction
2. Derived Quantities: Derived quantities are those obtained by simple combination of fundamental quantities and unit.
b. DERIVED QUANTITIES AND UNIT
| QUANTITY | DERIVATION | UNIT |
|---|---|---|
| Area | Length x breath | m2 |
| Volume | Length X breath X height | m3 |
| Density | Mass/volume | Kg/m3 |
| Speed | Distance x time | m/s |
| Velocity | Displacement/time | m/s |
| Acceleration | Change in velocity/Time | m/s2 |
| Force | Mass X Acceleration | N( Newton) |
| Pressure | Force/Area | Pascal/ Nm/s2 |
| Power | Work/time | watt |
C. MASS AND WEIGHT -
*Mass: Quantity of matter in a body. Constant everywhere. Measured in kg with a beam balance. Scalar quantity.
*Weight: Force of gravity acting on a mass. W = mg. Measured in Newton (N) with a spring balance. It changes with location. Vector quantity. g = 9.8m/s²
SUBMULTIPLE AND MULTIPLE UNIT:
| SUBMULTIPLE | PREFIX |
|---|---|
| 10-1 | Deci |
| 10-2 | Centi |
| 10-3 | Milli |
| 10-6 | Micro |
| 10-9 | Nano |
| 10-12 | Pico |
| MULTIPLE | PREFIX |
|---|---|
| 10 | Deca |
| 102 | Hecto |
| 103 | Kilo |
| 106 | Mega |
| 109 | Giga |
| 1012 | Tera |
D. DIMENSIONAL ANALYSIS
Dimension represents how a derived unit depends on fundamental quantities. We use M for Mass, L for Length, T for Time, I for Current.
Fundamental Dimensions:
Length =, Mass =, Time =, Current =[L][M][T][I]
Deriving Dimensions:
- Area = L x L = [L²]
- Volume = L³ = [L³]
- Velocity = Length/Time = L/T = [LT⁻¹]
- Acceleration = Velocity/Time = [LT⁻²]
- Force = mass x acceleration = M x LT⁻² = [MLT⁻²]
- Work/Energy = Force x distance = MLT⁻² x L = [ML²T⁻²]
- Power = Work/Time = [ML²T⁻³]
- Electric Charge = Current x Time = [IT]
E. USES of Dimensional Analysis:
1. To check correctness of an equation (Principle of Homogeneity - both sides must have same dimension)
2. To derive relationship between physical quantities
3. To convert from one unit system to another
Example: Check if v = at is dimensionally correct.
v = [LT⁻¹], a = [LT⁻²], t =
at = [LT⁻²] = [LT⁻¹] = v. So it's correct.[T]
Evaluation
OBJECTIVE QUESTIONS
1. Which of these is NOT a physical quantity?
A) Length
B) Kindness
C) Mass
D) Time
2. The SI unit of mass is:
A) Gram
B) Kilogram
C) Newton
D) Metre
3. The instrument used to measure electric current is:
A) Voltmeter
B) Ammeter
C) Thermometer
D) Barometer
4. Which of these is a derived quantity?
A) Mass
B) Length
C) Area
D) Time
5. The dimension of velocity is:
A) LT^-1
B) [LT-2
C) L2
D) MLT-2
6. Weight is measured with:
A) Beam balance
B) Chemical balance
C) Spring balance
D) Metre rule
7. The SI unit of electric current is:
A) Volt
B) Ampere
C) Ohm
D) Coulomb
8. A boy says his weight is 50kg. He is wrong because:
A) Weight is measured in Newton
B) Weight is measured in kg
C) Weight has no unit
D) His mass is too small
[MLT^{-2}] is the dimension of:
A) Work
B) Power
C) Force
D) Pressure
10. Which of these is measured with a Vernier Caliper?
A) Length of classroom
B) Diameter of a wire
C) Weight of a stone
D) Time for 100m race
Theory Questions
1. a) Define physical quantities and list the 7 fundamental quantities with their SI units.
1 b) Differentiate between:
i) Mass and Weight
ii) Fundamental and Derived quantities
Give 2 examples of derived quantities with their units.
2a) What is dimensional analysis? State two uses of dimensional analysis.
2b) Derive the dimensions of:
i) Force (F=ma)
ii) Work (Work = Force x distance)
iii) Use dimensional analysis to check if the equation $v = at$ is correct, where v is velocity, a is acceleration and t is time.