Laws of Motion — Class Notes

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ICSE Class 9 Physics • Concise Class Notes

1. Force

Definition A force is an external push or pull that changes or tends to change the state of rest or motion of a body, or changes its shape.
Unit: Newton (N) | Type: Vector | 1 N = 1 kg·m/s²

Effects of Force

Start motion (stationary → moving)
Stop or slow down motion
Change speed of moving body
Change direction of motion
Change shape or size of body

Contact Forces Muscular · Friction · Normal Reaction · Tension · Air Resistance

Non-Contact Forces Gravitational · Magnetic · Electrostatic

Balanced Forces (Net F = 0) No change in state. Body stays at rest or moves at constant velocity. Example: Book on table

Unbalanced Forces (Net F ≠ 0) Body accelerates in direction of net force. Example: Car accelerating

2. Newton's First Law — Law of Inertia

Statement ICSE "A body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force."

Inertia The natural tendency of a body to resist change in its state of rest or motion.
Greater mass = Greater Inertia | Mass is the measure of inertia.

Fig. 1 — Three types of Inertia with real-life examples.

Type	Description	Examples
Inertia of Rest	Tendency to remain at rest	Coin stays when card flicked; dust falls off beaten carpet; passenger jerks backward when bus starts
Inertia of Motion	Tendency to continue moving	Person falls forward when bus stops; bullet continues after leaving gun; athlete runs before long jump
Inertia of Direction	Tendency to continue in same direction	Passengers lean outward on turning bus; mud flies tangentially from bicycle wheel

3. Momentum

Definition $$p = mv$$ Unit: kg·m/s | Type: Vector (direction of velocity)

Solved Example Numerical A car (mass 1200 kg) at 72 km/h. Find momentum.

v = 20 m/s | p = 1200 × 20 = 24,000 kg·m/s

4. Newton's Second Law — F = ma

Statement ICSE "The rate of change of momentum of a body is directly proportional to the applied force, in the direction of the force."

Fig. 2 — Derivation of F = ma from rate of change of momentum.

$$F = ma = \frac{m(v-u)}{t} = \frac{\Delta p}{t}$$ 1 Newton = force giving 1 kg mass an acceleration of 1 m/s²

Solved Examples Numerical Q1: 500 N acts on 25 kg from rest for 4 s. Find v and s.

a = 20 m/s² | v = 80 m/s | s = 160 m

Q2: 1000 kg car at 20 m/s stops in 5 s. Find retarding force.

a = −4 m/s² | F = 4000 N

5. Impulse

Definition $\text{Impulse} = F \times t = \Delta p = m(v-u)$ Unit: N·s
Large force, short time = same impulse as small force, long time.

Applications Reduce force (increase time): Cricketer pulls hand back catching ball · Crumple zones in cars · Landing on cushion
Increase force (decrease time): Karate chop · Hammering a nail

6. Newton's Third Law — Action-Reaction

Statement ICSE "For every action there is an equal and opposite reaction. Action and reaction act on different bodies simultaneously." $$F_{AB} = -F_{BA}$$

Fig. 3 — Action-Reaction pairs: Rocket, Swimming, Walking, Gun Recoil.

⚠️ Key Misconception Action and reaction do NOT cancel each other because they act on different bodies. Only forces on the same body can cancel.

Situation	Action	Reaction
Walking	Foot pushes ground backward	Ground pushes person forward
Rocket	Exhaust gases expelled backward	Rocket moves forward
Gun fired	Bullet propelled forward	Gun recoils backward
Swimming	Arms push water backward	Water pushes swimmer forward

7. Law of Conservation of Momentum

Statement ICSE "In the absence of an external force, the total momentum of a system remains constant." $$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$

Fig. 4 — Momentum before collision = momentum after collision.

Solved Examples Numerical ICSE Q1 (Collision): 2 kg ball at 5 m/s hits 3 kg at rest; they stick together. Find common velocity.

$5v = 2(5) + 3(0) = 10$ → v = 2 m/s

Q2 (Gun Recoil): 4 kg rifle fires 50 g bullet at 200 m/s. Find recoil velocity.

$0 = 0.05 \times 200 + 4v_r$ → $v_r = $ −2.5 m/s

Q3 (Explosion): 10 kg bomb at rest explodes into 4 kg and 6 kg. 4 kg piece at 15 m/s. Find 6 kg velocity.

$0 = 4(15) + 6v$ → $v = $ −10 m/s

8. Formula Quick Reference

Quantity	Formula	Unit
Momentum	$p = mv$	kg·m/s
Newton's 2nd Law	$F = ma = m(v-u)/t = \Delta p/t$	N
Impulse	$J = F \times t = \Delta p = m(v-u)$	N·s
Conservation	$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$	—
Weight	$W = mg$	N
3rd Law	$F_{AB} = -F_{BA}$	—
Unit conversion	km/h × 5/18 = m/s \| m/s × 18/5 = km/h	—

9. Practice Problems

Q1 ICSE Explain why a passenger jerks backward when a bus starts suddenly.

Due to inertia of rest — the upper body tends to stay at rest while the seat (lower body) moves forward with the bus.

Q2 Numerical A 5 kg object starts from rest. A force acts for 3 s and gives it a velocity of 12 m/s. Find the force.

a = 12/3 = 4 m/s² | F = 5 × 4 = 20 N

Q3 Numerical A 0.2 kg ball hits a wall at 10 m/s and rebounds at 8 m/s. Contact time = 0.04 s. Find force.

$\Delta p = 0.2(-8-10) = -3.6$ N·s | F = 3.6/0.04 = 90 N

Q4 Numerical Two trolleys (4 kg at 3 m/s and 2 kg at rest) collide and move together. Find final velocity.

$(4+2)v = 4(3) + 2(0) = 12$ → $v = $ 2 m/s

Q5 ICSE Why does a rocket move in space even though there is no air to push against?

By Newton's Third Law, the rocket expels hot gases backward (action). The gases exert an equal and opposite force on the rocket (reaction), pushing it forward. The rocket does not need air — it pushes gases, not air.

10. Exam Tips & Common Mistakes

⚠️ Avoid These Mistakes

Action and reaction do NOT cancel (they act on DIFFERENT bodies)
Always define +ve and −ve direction before solving momentum problems
Recoil/explosion: total initial momentum = 0 if both bodies at rest
Do NOT forget to convert km/h → m/s before calculation
Mass (kg) ≠ Weight (N). Weight = mg.
Inertia ≠ Momentum. Inertia is a property; momentum is mass × velocity.

🎯 ICSE Exam Strategy

Definitions: All three laws + inertia + momentum — state standard definitions with formulas
Derivations: F = ma from Second Law; Conservation from Third Law — step by step
Numericals: Write Given → Find → Formula → Steps → Answer (with unit + direction)
Applications: Bus jerks, seatbelts, rocket, gun recoil, swimming — explain using which law
Conservation problems: Both "stick together" and "bounce back" types are equally important