PHYSICS. LINEAR MOMENTUM LECTURE

PHYSICS: MOMENTUM AND LAWS OF MOTION

1. Momentum

Momentum is the quantity of motion of a body. It depends on the mass of the body and its velocity.

Formula: Momentum (p) = mass (m) × velocity (v)

p = m × v

Momentum is measured in kilogram metre per second (kg m/s).

2. Laws of Motion (Newton’s Laws)

First Law

A body will remain at rest or continue to move with uniform speed in a straight line unless acted upon by an external force.

Second Law

The rate of change of momentum of a body is directly proportional to the force applied and occurs in the direction of the force.

Third Law

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

3. Law of Conservation of Momentum

The total momentum of a system remains constant if no external force acts on it.

Diagram Explanation:

Before collision: A → → ← ← B

After collision: A ← ← → → B

4. Inertial Mass and Weight

Inertial Mass: This is the resistance of a body to change its state of motion.

Weight: This is the force of gravity acting on a body.

Weight = mass × gravitational acceleration (W = mg)

5. Types of Collision

Elastic Collision

In elastic collision, both momentum and kinetic energy are conserved.

Inelastic Collision

In inelastic collision, momentum is conserved but kinetic energy is not conserved.

6. Solved Calculations

Elastic Collision Example

Mass of A = 2 kg, velocity = 4 m/s

Momentum = 2 × 4 = 8 kg m/s

Total momentum before collision = total momentum after collision

Inelastic Collision Example

Mass of A = 3 kg, velocity = 2 m/s

Mass of B = 1 kg, velocity = 0 m/s

Total momentum = (3×2) + (1×0) = 6 kg m/s

7. Equations of Motion

The equations of motion are used to solve problems involving uniformly accelerated motion.

• First equation: v = u + at
• Second equation: s = ut + ½ at²
• Third equation: v² = u² + 2as

Where:
u = initial velocity,
v = final velocity,
a = acceleration,
t = time,
s = distance travelled.

8. Kinetic Energy

Kinetic energy is the energy possessed by a body due to its motion.

Kinetic Energy (KE) = ½ mv²

9. Kinetic Energy in Collisions

Elastic Collision

In elastic collision, both momentum and kinetic energy are conserved.

KE before collision = KE after collision

½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²

Inelastic Collision

In inelastic collision, momentum is conserved but kinetic energy is not conserved.

KE before collision > KE after collision

Some kinetic energy is lost as heat, sound, or deformation.

10. Summary: Conservation Conditions

• Only momentum conserved: In inelastic collisions
• Momentum and kinetic energy conserved: In elastic collisions