MOMENTUM is a property of any moving object โ it depends on both mass and velocity.
EQUATION:
p = m ร v
p = momentum (kg m/s)
m = mass (kg)
v = velocity (m/s)
Momentum is a VECTOR quantity โ it has both magnitude and direction.
Direction of momentum = direction of velocity.
EXAMPLES:
1000 kg car at 20 m/s: p = 1000 ร 20 = 20,000 kg m/s
0.5 kg cricket ball at 40 m/s: p = 0.5 ร 40 = 20 kg m/s
The car has 1000ร more momentum despite same speed โ mass matters greatly.
Link to Newton's Second Law:
Force = rate of change of momentum = ฮp รท ฮt = mฮv รท ฮt = 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 โ two objects collide and stick together or bounce apart.
EXPLOSIONS โ 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 ร 10) + (800 ร 0) = 10,000 kg m/s
After: p_total = (1000 + 800) ร v = 1800v
10,000 = 1800 ร v
v = 10,000 รท 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 ร 500) + (1.9 ร v) = 0
50 + 1.9v = 0
v = โ50 รท 1.9 = โ26.3 m/s (negative = backward)
Momentum, Force and Safety
IMPULSE โ changing momentum requires a force:
F ร t = ฮp (impulse = change in momentum)
F = ฮp รท t
To stop an object with a given momentum:
LONGER TIME โ SMALLER FORCE required.
SHORTER TIME โ LARGER FORCE.
SAFETY APPLICATIONS:
CRUMPLE ZONES: car crushes slowly on impact โ increases time of collision โ reduces peak force on occupants.
SEAT BELTS: stretch slightly โ increase time for passenger to decelerate โ reduce peak force.
AIR BAGS: passenger's head decelerates into cushion of air โ longer time โ smaller force on head.
HELMETS: foam compresses on impact โ longer stopping time โ reduced force on skull.
CATCHING: a cricket ball caught by 'giving' with hands โ increases time โ reduces force.
CYCLING HELMETS: foam liner increases stopping time for head in a crash.
All use the same principle: ฮp is fixed (same change in momentum needed) โ increasing time reduces the force.
โ ๏ธ Common Mistake
Momentum is a VECTOR โ 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.
๐ 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)
๐ Key Equations
p = m ร v
Conservation: total p before = total p after
Impulse: F ร t = ฮp
๐ Key Note
p = mv. Vector โ direction matters. Conservation: total p before = total p after (closed system). Applies to collisions and explosions. Impulse: F = ฮp/t. Longer collision time โ smaller force. Safety: crumple zones, airbags, seat belts, helmets all increase collision time.
๐ฏ Matching Activity โ Momentum Calculations
Match each scenario to the correct momentum or velocity. โ 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
1000 kg + 800 kg after collision (p = 10,000 kg m/s) โ v = 10000/1800
1000 kg car at 20 m/s โ p = 1000 ร 20
Total momentum before an explosion โ object was stationary
Increase collision time โ reduce peak force โ same impulse, longer time
โฝ 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: mโvโ + mโvโ = (mโ+mโ)v
I
p before = (600 ร 15) + (400 ร 0) = 9000 kg m/s
F
9000 = (600 + 400) ร v = 1000v
A
v = 9000 รท 1000 = 9 m/s
๐ฏ 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?
โญ How Well Do You Understand This Topic?
Be honest with yourself โ this helps you know what to revise!
Don't get itGetting thereNailed it!
๐ค Ask Mr Badmus AI
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I'll use FIFA for calculations and flag Higher/Triple content clearly.