Physics begins with measurement. Every physical quantity – length, mass, time, force or energy – must be measured in a fixed unit, and its nature can be expressed through its dimensions. Once we can measure motion correctly, Newton's three laws of motion explain why objects move, stop or change direction. This chapter is one of the most frequently asked areas in the General Science section of WBCS, SSC, Railway, Police and Banking exams.
Physical Quantities
A quantity that can be measured and expressed in numbers is called a physical quantity. Every measurement has two parts: a number and a unit. For example, in "5 metres", 5 is the number and metre is the unit.
- Fundamental (base) quantities – independent quantities that do not depend on any other quantity, such as length, mass and time.
- Derived quantities – quantities obtained from fundamental quantities, such as speed (length ÷ time), area (length × length) and force (mass × acceleration).
Scalar and Vector Quantities
| Scalar | Vector |
|---|---|
| Has only magnitude | Has both magnitude and direction |
| Added by simple arithmetic | Added by vector rules (triangle / parallelogram law) |
| Examples: mass, speed, distance, time, work, energy, temperature, power, pressure | Examples: displacement, velocity, acceleration, force, momentum, weight, torque, impulse |
Exam point: Electric current has both magnitude and direction but is treated as a scalar, because it does not follow the laws of vector addition.
Systems of Units
| System | Length | Mass | Time |
|---|---|---|---|
| CGS (French system) | centimetre | gram | second |
| FPS (British system) | foot | pound | second |
| MKS (Metric system) | metre | kilogram | second |
| SI (International System) | metre | kilogram | second |
The International System of Units (SI) was adopted in 1960 by the 11th General Conference on Weights and Measures (CGPM). It is now used all over the world for science and trade.
Seven SI Base Units
| Physical quantity | SI unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Earlier, radian (plane angle) and steradian (solid angle) were called supplementary units. Since 1995 they are treated as dimensionless derived units.
Did you know? On 20 May 2019 (World Metrology Day), all SI base units were redefined using fixed values of nature's constants. The kilogram is now defined using the Planck constant, replacing the metal cylinder (International Prototype Kilogram) kept in France since 1889.
Important Derived SI Units
| Quantity | SI unit | In base units |
|---|---|---|
| Force | newton (N) | kg m s-2 |
| Work / Energy | joule (J) | N m = kg m2 s-2 |
| Power | watt (W) | J s-1 |
| Pressure | pascal (Pa) | N m-2 |
| Frequency | hertz (Hz) | s-1 |
| Electric charge | coulomb (C) | A s |
| Electric potential | volt (V) | J C-1 |
| Electrical resistance | ohm (Ω) | V A-1 |
| Electrical conductance | siemens (S) | Ω-1 |
| Capacitance | farad (F) | C V-1 |
| Magnetic flux | weber (Wb) | V s |
| Magnetic field (flux density) | tesla (T) | Wb m-2 |
| Inductance | henry (H) | Wb A-1 |
| Luminous flux | lumen (lm) | cd sr |
| Illuminance | lux (lx) | lm m-2 |
| Radioactivity | becquerel (Bq) | s-1 |
| Absorbed radiation dose | gray (Gy) | J kg-1 |
| Equivalent radiation dose | sievert (Sv) | J kg-1 |
Practical Units You Must Remember
| Unit | Measures | Value |
|---|---|---|
| Light year | Distance (astronomical) | 9.46 × 1015 m – distance travelled by light in one year |
| Astronomical Unit (AU) | Distance | 1.496 × 1011 m – mean Earth–Sun distance |
| Parsec | Distance | 3.26 light years ≈ 3.08 × 1016 m (largest practical unit of distance) |
| Angstrom (Å) | Wavelength, atomic size | 10-10 m |
| Fermi (fm) | Nuclear size | 10-15 m |
| Micron (µm) | Length | 10-6 m |
| Nautical mile | Sea / air distance | 1852 m |
| Knot | Speed of ships | 1 nautical mile per hour |
| Horsepower (hp) | Power | 746 W |
| Kilowatt-hour (kWh) | Electrical energy ("1 unit") | 3.6 × 106 J |
| Calorie | Heat energy | ≈ 4.2 J (4.186 J) |
| Electron volt (eV) | Energy of particles | 1.6 × 10-19 J |
| Atmosphere (atm) | Pressure | 1.013 × 105 Pa = 76 cm of mercury |
| Bar | Pressure | 105 Pa |
| Torr | Pressure | 1 mm of mercury |
| Carat | Mass of gems | 200 mg |
| Quintal / Metric tonne | Mass | 100 kg / 1000 kg |
| Decibel (dB) | Intensity of sound | Logarithmic unit |
Temperature conversion: C/5 = (F − 32)/9 and K = C + 273.15. Celsius and Fahrenheit scales read the same at −40°. Normal human body temperature is about 37°C = 98.6°F = 310 K.
SI Prefixes
| Prefix | Symbol | Value | Prefix | Symbol | Value |
|---|---|---|---|---|---|
| deca | da | 101 | deci | d | 10-1 |
| hecto | h | 102 | centi | c | 10-2 |
| kilo | k | 103 | milli | m | 10-3 |
| mega | M | 106 | micro | µ | 10-6 |
| giga | G | 109 | nano | n | 10-9 |
| tera | T | 1012 | pico | p | 10-12 |
| peta | P | 1015 | femto | f | 10-15 |
| exa | E | 1018 | atto | a | 10-18 |
In 2022, four new prefixes were added: ronna (1027), quetta (1030), ronto (10-27) and quecto (10-30).
Dimensions and Dimensional Formula
The dimensions of a physical quantity are the powers to which the fundamental quantities must be raised to express it. In mechanics we use mass [M], length [L] and time [T]. For example, velocity = length ÷ time, so its dimensional formula is [M0 L1 T-1].
| Quantity | Formula | Dimensional formula |
|---|---|---|
| Area | length × breadth | [M0 L2 T0] |
| Volume | l × b × h | [M0 L3 T0] |
| Density | mass / volume | [M L-3 T0] |
| Velocity / Speed | distance / time | [M0 L T-1] |
| Acceleration | velocity / time | [M0 L T-2] |
| Force | mass × acceleration | [M L T-2] |
| Momentum | mass × velocity | [M L T-1] |
| Impulse | force × time | [M L T-1] |
| Work / Energy | force × distance | [M L2 T-2] |
| Power | work / time | [M L2 T-3] |
| Pressure / Stress | force / area | [M L-1 T-2] |
| Frequency | 1 / time period | [M0 L0 T-1] |
| Surface tension | force / length | [M L0 T-2] |
| Planck's constant | energy / frequency | [M L2 T-1] |
| Gravitational constant (G) | F r2 / m1m2 | [M-1 L3 T-2] |
Quantities with the Same Dimensions
- Momentum and Impulse – [M L T-1]
- Work, Energy and Torque – [M L2 T-2]
- Pressure, Stress and Young's modulus – [M L-1 T-2]
- Planck's constant and Angular momentum – [M L2 T-1]
- Frequency, Angular velocity and Velocity gradient – [T-1]
Dimensionless Quantities
Strain, refractive index, relative density (specific gravity), angle, coefficient of friction and relative permittivity have no dimensions.
Uses and Limits of Dimensional Analysis
- Principle of homogeneity: in a correct equation, every term must have the same dimensions. This is used to check whether a formula is correct.
- To convert a quantity from one system of units to another.
- To derive a simple relation between physical quantities.
- Limitation: it cannot find the value of dimensionless constants (like ½ or 2π), and cannot handle equations with trigonometric, exponential or logarithmic terms.
Newton's Laws of Motion
Sir Isaac Newton stated the three laws of motion in his book Philosophiæ Naturalis Principia Mathematica, published in 1687. Before him, Galileo Galilei had shown through experiments on inclined planes that a moving body keeps moving unless something stops it – the idea of inertia.
First Law of Motion – Law of Inertia
Statement: An object remains in its state of rest or of uniform motion in a straight line unless an external unbalanced force acts on it.
The tendency of a body to resist a change in its state of rest or motion is called inertia. Mass is the measure of inertia – a heavier body has more inertia. The first law also gives the definition of force.
| Type of inertia | Everyday example |
|---|---|
| Inertia of rest | Passengers fall backward when a stopped bus suddenly starts; dust comes out when a carpet is beaten; a coin on a card falls into the glass when the card is flicked away. |
| Inertia of motion | Passengers fall forward when a moving bus brakes suddenly; an athlete runs some distance before a long jump; a person jumping from a moving bus falls forward. |
| Inertia of direction | Passengers lean outward when a vehicle takes a sharp turn; mud flies off a rotating wheel along the tangent. |
This is why seat belts are compulsory in cars – they stop our body from moving forward due to inertia of motion during sudden braking.
Second Law of Motion – Law of Force
Statement: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
F = ma (force = mass × acceleration), where momentum p = mv.
- 1 newton is the force that produces an acceleration of 1 m/s2 in a body of mass 1 kg.
- The second law gives the measure (magnitude) of force.
- Impulse = force × time = change in momentum. Its SI unit is N s.
Applications of impulse: to reduce the force on our hands, a cricketer pulls his hands backward while catching a fast ball – this increases the time of impact. For the same reason, high jumpers land on soft cushions or sand, vehicles have shock absorbers, and glassware is packed in straw or thermocol.
Third Law of Motion – Law of Action and Reaction
Statement: To every action there is an equal and opposite reaction.
Action and reaction always act on two different bodies, so they never cancel each other.
- A gun recoils backward when a bullet is fired.
- A rocket moves up by pushing hot gases downward. Jet planes work on the same principle.
- While walking, we push the ground backward and the ground pushes us forward.
- A swimmer pushes water backward to move forward.
- A boat moves backward when a person jumps from it to the shore.
Law of Conservation of Momentum
When no external force acts on a system, its total momentum remains constant. This law follows from Newton's second and third laws. The recoil of a gun and the motion of a rocket are both explained by conservation of momentum.
Mass and Weight
| Mass | Weight |
|---|---|
| Quantity of matter in a body | Force with which the Earth pulls the body (W = mg) |
| Scalar quantity, SI unit kg | Vector quantity, SI unit newton |
| Same everywhere | Changes from place to place |
| Measured by a beam (physical) balance | Measured by a spring balance |
The weight of a body on the Moon is about one-sixth of its weight on the Earth, but its mass remains the same.
Quick Revision Points
- SI was adopted in 1960 and has 7 base units.
- Largest practical unit of distance: parsec; light year is a unit of distance, not time.
- 1 horsepower = 746 W; 1 kWh = 3.6 × 106 J.
- Momentum and impulse have the same dimensions.
- Newton's first law defines force; the second law measures force.
- Action and reaction act on different bodies.
- Rocket propulsion is based on the third law and conservation of momentum.
Read also: Force and its Types
Practice MCQs
1. Which of the following is NOT an SI base unit?
(a) Kelvin
(b) Candela
(c) Newton
(d) Mole
2. Light year is a unit of:
(a) Time
(b) Distance
(c) Speed of light
(d) Intensity of light
3. 1 horsepower is equal to:
(a) 500 W
(b) 746 W
(c) 1000 W
(d) 846 W
4. The dimensional formula [M L T-1] belongs to:
(a) Force
(b) Work
(c) Momentum
(d) Power
5. Which pair has the same dimensions?
(a) Work and Power
(b) Force and Pressure
(c) Work and Torque
(d) Momentum and Energy
6. At what temperature do Celsius and Fahrenheit scales show the same reading?
(a) 0°
(b) −40°
(c) 40°
(d) −273°
7. Passengers fall forward when a moving bus stops suddenly. This is due to:
(a) Inertia of rest
(b) Inertia of motion
(c) Inertia of direction
(d) Third law of motion
8. A cricketer pulls his hands back while catching a ball to:
(a) Reduce the momentum of the ball
(b) Increase the time of impact and reduce force
(c) Increase the force
(d) Change the direction of the ball
9. The working of a rocket is based on:
(a) Newton's first law
(b) Conservation of energy
(c) Newton's third law
(d) Law of gravitation
10. Newton's laws of motion were published in which book?
(a) Opticks
(b) Principia Mathematica
(c) Dialogue Concerning the Two Chief World Systems
(d) Micrographia
Answers: 1 – (c) | 2 – (b) | 3 – (b) | 4 – (c) | 5 – (c) | 6 – (b) | 7 – (b) | 8 – (b) | 9 – (c) | 10 – (b)
Reference: NCERT Physics, Class IX (Force and Laws of Motion) and Class XI (Units and Measurements; Laws of Motion); BIPM SI Brochure.