MomentumAQA GCSE Physics: Revision notes
Section 1
What is momentum and how is it calculated?
Momentum is a measure of how difficult it is to stop a moving object. It depends on both the mass and velocity of the object.
Momentum is calculated using the equation:
p = mv
Where:
- p = momentum (measured in kg m/s or N s)
- m = mass (measured in kg)
- v = velocity (measured in m/s)
Key points:
- Momentum is a vector quantity, meaning it has both magnitude and direction
- A larger mass or higher velocity results in greater momentum
- Momentum is always in the same direction as the velocity
- The SI unit for momentum is kg m/s (kilogram metres per second)
A car of mass 1200 kg travelling at 25 m/s has momentum p = 1200 × 25 = 30,000 kg m/s. A person of mass 60 kg running at 8 m/s has momentum p = 60 × 8 = 480 kg m/s. The car has far greater momentum because of its much larger mass.
Momentum is like the 'oomph' of a moving object. A heavy lorry moving slowly can have more 'oomph' than a light car moving fast—it depends on both how heavy and how fast.
Section 2
What is the principle of conservation of momentum?
The principle of conservation of momentum states that in a closed system (where no external forces act), the total momentum before an event equals the total momentum after the event.
In equation form:
Total momentum before = Total momentum after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where:
- u = velocity before collision
- v = velocity after collision
- Subscripts 1 and 2 refer to different objects
Important conditions:
- The system must be isolated (no external forces like friction acting significantly)
- Momentum is conserved in all types of collisions: elastic and inelastic
- In explosions, total momentum is also conserved (often starting from zero)
Examiners expect you to clearly state 'momentum is conserved' and set up the equation with correct subscripts for 'before' and 'after'. Always check that your final answer has units (kg m/s) and makes physical sense.
Students often forget that momentum is a vector and direction matters. If objects move in opposite directions, velocities have opposite signs. Forgetting this leads to incorrect calculations.
Section 3
How do forces change momentum?
A force acting on an object for a time period causes a change in momentum. This relationship is expressed as:
F = Δp/Δt
Or rearranged:
FΔt = Δp
Where:
- F = force (measured in N, newtons)
- Δp = change in momentum (measured in kg m/s)
- Δt = time interval (measured in seconds)
- FΔt = impulse (the product of force and time)
Key understanding:
- The larger the force or the longer it acts, the greater the change in momentum
- A small force acting for a long time can produce the same momentum change as a large force acting briefly
- Impulse has units of N s (newton seconds) or equivalently kg m/s
Deriving the equation:
Starting from Newton's second law, F = ma, and using a = Δv/Δt:
- F = m(Δv/Δt)
- F = (mΔv)/Δt
- Since p = mv, then Δp = mΔv
- Therefore: F = Δp/Δt
A tennis ball of mass 0.06 kg moving at 20 m/s is stopped in 0.1 s. Change in momentum Δp = 0.06 × (0 − 20) = −1.2 kg m/s. Force required: F = 1.2 / 0.1 = 12 N. A larger stopping time would require a smaller force.
Section 4
How does F = mΔv/Δt relate to safety features?
F = mΔv/Δt is the alternative form of Newton's second law showing that force depends on how quickly momentum changes.
Safety features work by increasing Δt (the time interval) to reduce the force experienced during collisions:
| Safety Feature | How it works | Effect on force |
|---|---|---|
| Crumple zones | Deforms during collision, extending impact time | Increases Δt, decreases F |
| Air bags | Inflate to cushion impact and extend time of collision | Increases Δt, decreases F |
| Seat belts | Restrain passenger gradually, spreading deceleration over time | Increases Δt, decreases F |
| Padding in helmets | Compresses during impact, prolonging collision | Increases Δt, decreases F |
The principle:
Since F = mΔv/Δt:
- If Δv (change in velocity) is fixed, increasing Δt decreases F
- Lower forces mean less injury to passengers
- Even though the same momentum change occurs, spreading it over a longer time reduces peak force
Real-world analogy: Catching a cricket ball by pulling your hand back (increasing Δt) is less painful than catching it with a rigid arm (decreasing Δt)—same momentum change, different force.
Examiners reward clear explanation of how increasing time reduces force. State: 'Crumple zones increase Δt, so for the same Δv and m, F = mΔv/Δt becomes smaller, reducing injury.'
Section 5
How do you apply conservation of momentum to collisions?
Step-by-step approach to collision problems:
- Identify the system – which objects are involved?
- State the principle – 'Momentum is conserved because there are no external forces'
- Assign directions – choose positive and negative directions (e.g., left is positive)
- Write before and after equations:
- Total momentum before = m₁u₁ + m₂u₂
- Total momentum after = m₁v₁ + m₂v₂
- Set them equal and solve for the unknown
- Check your answer – does the sign make sense? Are units correct?
Types of collisions:
- Elastic collisions: Both momentum and kinetic energy are conserved (objects bounce apart)
- Inelastic collisions: Momentum is conserved but kinetic energy is not (some energy lost to deformation, sound, heat)
- Explosions: Objects start together (u = 0) and move apart; momentum is conserved
Common scenarios:
- Two objects colliding head-on (use opposite signs for velocities)
- Two objects colliding and sticking together (final velocity is the same for both)
- Objects separating in an explosion (initial momentum may be zero)
Car A (1500 kg, 8 m/s) collides with stationary Car B (1200 kg). They stick together. Find final velocity. Before: p = 1500(8) + 1200(0) = 12,000 kg m/s. After: p = (1500 + 1200)v. Setting equal: 12,000 = 2700v, so v = 4.44 m/s.
Must Know
- Momentum p = mv (in kg m/s); momentum is a vector quantity with direction
- Conservation of momentum: total momentum before = total momentum after in a closed system; applies to all collisions and explosions
- Impulse F = Δp/Δt or FΔt = Δp; relates force, time, and momentum change
- Alternative form F = mΔv/Δt shows that force depends on how quickly momentum changes
- Safety features (crumple zones, air bags, seat belts) work by increasing Δt to reduce peak force during collisions, protecting occupants
- In collision problems, always assign directions carefully (use positive/negative signs), state that momentum is conserved, and set initial momentum equal to final momentum
That's the notes covered.
Carry on to the next subtopic.