📖 In-Depth Theory
What Is Momentum?
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.