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Momentum

🌟 IGCSE Physics Topic 1.6: Momentum​

🔹 1. Definition of Momentum​

Momentum is the quantity of motion an object has. It depends on both its mass and velocity.

  • p = momentum (kg·m/s)
  • m = mass (kg)
  • v = velocity (m/s)

✅ Key idea:
An object with more mass or moving faster has more momentum.

🔸 Example 1:​

A car of mass 1000 kg moves at 20 m/s. Find its momentum.

p = mv = 1000 20 = 20,000 kg·m/s

So, the car’s momentum is 20,000 kg·m/s.

⚡ Important Notes:​

  • Momentum is a vector quantity – it has both magnitude and direction.

  • If an object is moving to the left or backwards, its momentum is negative.

  • Momentum increases with speed and mass.

🔹 2. Impulse​

Impulse is the change in momentum of an object when a force acts on it for a period of time.

✅ Impulse = change in momentum

  • F = force (N)
  • Δt = time (s)
  • Δ(mv) = change in momentum (kg·m/s)

🔸 Example 2:​

A bat applies a force of 50 N to a ball for 0.2 s.
Find the impulse.

Impulse= FΔt = 50 0.2 = 10 N·s

➡️ The ball’s momentum changes by 10 kg·m/s.

⚡ Units:​

  • Momentum → kg·m/s
  • Impulse → N·s

1 N·s = 1 kg·m/s

🔹 3. Principle of Conservation of Momentum​

The total momentum before a collision = total momentum after the collision
(Provided no external forces act on the system, such as friction or air resistance)

Where:

✅ Momentum is always conserved in:

  • Collisions (elastic or inelastic)
  • Explosions

However, kinetic energy might not be conserved (e.g., inelastic collisions).

🔸 Example 3: Collision​

A 0.5 kg trolley moving at 4 m/s hits a 1.5 kg stationary trolley.
They stick together after collision.

✅ The two trolleys move together at 1 m/s after collision.

🔸 Example 4: Explosion​

A rifle (mass = 4 kg) fires a bullet (mass = 0.02 kg) at 200 m/s.
Find the recoil velocity of the rifle.

Before firing, total momentum = 0.
After firing:

✅ Rifle recoils backwards at 1 m/s.

🔹 4. Resultant Force and Change in Momentum​

From Newton’s Second Law:

  • F = resultant force (N)
  • Δp = change in momentum (kg·m/s)
  • Δt = time (s)

✅ This shows that a force causes a change in momentum.

🔸 Example 5:​

A force acts on a 2 kg object, changing its velocity from 3 m/s to 7 m/s in 2 seconds.
Find the force.

✅ Force = 4 N

💡 Everyday Applications of Momentum and Impulse​

  • Car airbags & crumple zones: Increase time of impact → reduce force.

  • Catching a ball: Hands move backward to increase impact time → less force on hands.

  • Seatbelts: Increase stopping time during crashes → reduce injury.

⚙️ Exam Tips​

✅ 1. Always include direction when working with momentum (e.g., right = positive, left = negative).
✅ 2. Check for total system: Momentum is conserved for the whole system, not individual objects.
✅ 3. Convert all units properly:

  • mass → kg

  • velocity → m/s
    ✅ 4. Be careful with signs:
    If one object moves in the opposite direction, its velocity should be negative.
    ✅ 5. Remember:
    Impulse = change in momentum → helps when given time or force instead of velocities.