Chapter 4: Laws of Motion

Chapter 4: Laws of Motion

1. Force and Inertia

• Force: Push or pull that changes state of motion
• Inertia: Resistance to change in motion
• Greater mass → greater inertia

2. Newton’s First Law

A body remains at rest or in uniform motion unless acted upon by an external force.

• Also called Law of Inertia

3. Momentum and Newton’s Second Law

• Momentum (p): p = mv
• Newton’s Second Law: Force = rate of change of momentum

F = ma

4. Impulse

Impulse is change in momentum.

Impulse = F × t = Change in Momentum

5. Newton’s Third Law

For every action, there is an equal and opposite reaction.

6. Law of Conservation of Momentum

Total momentum before collision = total momentum after collision

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

7. Equilibrium of Forces

• Net force = 0
• Body remains at rest or moves uniformly

8. Friction

Types

• Static friction
• Kinetic friction
• Rolling friction

Laws of Friction

• Friction ∝ Normal reaction
• Independent of area of contact

F = μN

Lubrication: Reduces friction

9. Uniform Circular Motion

• Velocity changes direction continuously
• Centripetal force acts toward center

F = mv²/r

10. Banking of Roads

• Vehicles move safely on curves due to centripetal force
• Banked roads reduce dependence on friction

11. MCQ One-Liners

• Inertia depends on mass.
• Unit of force is Newton.
• Momentum = mass × velocity.
• SI unit of momentum is kg·m/s.
• Force = ma.
• Impulse equals change in momentum.
• Action-reaction forces act on different bodies.
• Momentum is conserved in isolated system.
• Static friction is greater than kinetic friction.
• Rolling friction is minimum.
• Friction depends on normal reaction.
• Lubricants reduce friction.
• Centripetal force acts toward center.
• Unit of friction is Newton.
• Equilibrium means net force zero.
• Acceleration is zero in equilibrium.
• Friction opposes motion.
• Banking reduces need for friction.
• Impulse unit is N·s.
• Force changes momentum.

12. Numerical Problems with Solutions

1. Force Calculation

m = 5 kg, a = 2 m/s²

F = ma = 5×2 = 10 N

2. Momentum

m = 10 kg, v = 3 m/s

p = mv = 10×3 = 30 kg·m/s

3. Impulse

F = 20 N, t = 5 s

Impulse = 20×5 = 100 Ns

4. Friction Force

μ = 0.5, N = 10 N

F = μN = 0.5×10 = 5 N

5. Conservation of Momentum

m₁=2kg,u₁=3m/s; m₂=1kg,u₂=0

Initial momentum = 2×3 = 6
After collision:
6 = 2v₁ + v₂

6. Centripetal Force

m = 2 kg, v = 4 m/s, r = 2 m

F = mv²/r = 2×16/2 = 16 N

7. Acceleration

F = 20 N, m = 4 kg

a = F/m = 20/4 = 5 m/s²

8. Normal Reaction

m = 10 kg, g = 10

N = mg = 10×10 = 100 N