MOMENTUM is a property of any moving object — it depends on both mass and velocity.
EQUATION:
p = m × v
p = momentum (kg m/s)
m = mass (kg)
v = velocity (m/s)
Momentum is a VECTOR quantity — it has both magnitude and direction.
Direction of momentum = direction of velocity.
EXAMPLES:
1000 kg car at 20 m/s: p = 1000 × 20 = 20,000 kg m/s
0.5 kg cricket ball at 40 m/s: p = 0.5 × 40 = 20 kg m/s
The car has 1000× more momentum despite same speed — mass matters greatly.
Link to Newton's Second Law:
Force = rate of change of momentum = Δp ÷ Δt = mΔv ÷ Δt = ma
This is the more general form of F = ma.
Conservation of Momentum
In a CLOSED SYSTEM (no external forces), total momentum is CONSERVED.
Total momentum before event = Total momentum after event
This applies to:
COLLISIONS — two objects collide and stick together or bounce apart.
EXPLOSIONS — one stationary object breaks apart.
COLLISION EXAMPLE:
Car A (1000 kg) at 10 m/s hits stationary car B (800 kg). They stick together.
Before: p_total = (1000 × 10) + (800 × 0) = 10,000 kg m/s
After: p_total = (1000 + 800) × v = 1800v
10,000 = 1800 × v
v = 10,000 ÷ 1800 = 5.56 m/s
EXPLOSION EXAMPLE:
A 2 kg rocket at rest fires a 0.1 kg shell at 500 m/s forward.
Before: p_total = 0 (at rest)
After: p_shell + p_rocket = 0
(0.1 × 500) + (1.9 × v) = 0
50 + 1.9v = 0
v = −50 ÷ 1.9 = −26.3 m/s (negative = backward)
Momentum, Force and Safety
IMPULSE — changing momentum requires a force:
F × t = Δp (impulse = change in momentum)
F = Δp ÷ t
To stop an object with a given momentum:
LONGER TIME → SMALLER FORCE required.
SHORTER TIME → LARGER FORCE.
SAFETY APPLICATIONS:
CRUMPLE ZONES: car crushes slowly on impact → increases time of collision → reduces peak force on occupants.
SEAT BELTS: stretch slightly → increase time for passenger to decelerate → reduce peak force.
AIR BAGS: passenger's head decelerates into cushion of air → longer time → smaller force on head.
HELMETS: foam compresses on impact → longer stopping time → reduced force on skull.
CATCHING: a cricket ball caught by 'giving' with hands — increases time → reduces force.
CYCLING HELMETS: foam liner increases stopping time for head in a crash.
All use the same principle: Δp is fixed (same change in momentum needed) — increasing time reduces the force.
⚠️ Common Mistake
Momentum is a VECTOR — direction matters. When objects move in opposite directions, one momentum is negative. In conservation problems: always define a positive direction first, then assign signs accordingly. Total momentum is ZERO before an explosion (object at rest), so the two parts fly off with equal and opposite momenta.
📐 Variables
pMomentum (p) is measured in kg m/s (kg m/s)
mMass (m) is measured in kilograms (kg)
vVelocity (v) is measured in m/s (m/s)
📐 Key Equations
p = m × v
Conservation: total p before = total p after
Impulse: F × t = Δp
📌 Key Note
p = mv. Vector — direction matters. Conservation: total p before = total p after (closed system). Applies to collisions and explosions. Impulse: F = Δp/t. Longer collision time → smaller force. Safety: crumple zones, airbags, seat belts, helmets all increase collision time.
🎯 Matching Activity — Momentum Calculations
Match each scenario to the correct momentum or velocity. — drag the symbols on the right to match the component names on the left.
20,000 kg m/s
Drop here
5.56 m/s
Drop here
Crumple zones
Drop here
Zero
Drop here
Total momentum before an explosion — object was stationary
Increase collision time → reduce peak force — same impulse, longer time
1000 kg + 800 kg after collision (p = 10,000 kg m/s) — v = 10000/1800
1000 kg car at 20 m/s — p = 1000 × 20
⚽ FIFA Worked Examples
Conservation of Momentum
A 600 kg car travelling at 15 m/s collides with a stationary 400 kg car. They stick together. Find their velocity after the collision.
F
Total p before = total p after: m₁v₁ + m₂v₂ = (m₁+m₂)v
I
p before = (600 × 15) + (400 × 0) = 9000 kg m/s
F
9000 = (600 + 400) × v = 1000v
A
v = 9000 ÷ 1000 = 9 m/s
🎯 Test Yourself
Question 1 of 2
1. A 0.5 kg ball moving at 8 m/s collides with a stationary 1.5 kg ball. They stick together. What is their combined velocity?
2. Why do modern cars have crumple zones at the front?
⭐ How Well Do You Understand This Topic?
Be honest with yourself — this helps you know what to revise!
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🤖 Ask Mr Badmus AI
Stuck? Just ask! 💬
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