MomentumCambridge IGCSE Physics: Revision notes
Section 1
What is momentum and how do we calculate it?
Momentum is a measure of how difficult it is to stop a moving object. It is defined as the product of an object's mass and its velocity.
The equation is:
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 heavy object moving slowly can have the same momentum as a light object moving quickly
- Momentum is always in the same direction as the velocity
- If velocity is zero, momentum is zero, regardless of mass
A car of mass 1500 kg travels at 20 m/s. Calculate its momentum. p = mv = 1500 × 20 = 30,000 kg m/s or 30,000 N s.
Think of momentum as 'oomph' – a bowling ball rolling slowly has less oomph than the same ball rolling fast, and a car has more oomph than a bicycle at the same speed.
Section 3
How does resultant force relate to momentum and acceleration?
The resultant force can be defined in terms of momentum change. It is the rate of change of momentum.
The equation is:
F = Δp/Δt
Where:
- F = resultant force (measured in N)
- Δp = change in momentum (measured in kg m/s)
- Δt = time interval (measured in s)
This is equivalent to Newton's second law:
- Starting with F = Δp/Δt and substituting p = mv:
- F = Δ(mv)/Δt = mΔv/Δt = ma (assuming constant mass)
Key points:
- This form of Newton's second law is more fundamental than F = ma
- A large force is needed to produce a large momentum change in a short time
- A small force can produce the same momentum change if it acts for a longer time
- The resultant force is the net force after all forces are combined
A 2 kg object changes its momentum from 10 kg m/s to 50 kg m/s in 4 seconds. Resultant force = Δp/Δt = (50 − 10)/4 = 40/4 = 10 N.
Students often forget that Δp means 'final momentum minus initial momentum' – direction matters. If an object slows down, the change in momentum is negative, and so is the resultant force.
Section 4
What is the principle of conservation of momentum?
The principle of conservation of momentum states that the total momentum of a closed system remains constant, provided no external forces act on the system.
For a collision or interaction between two objects:
Total momentum before = Total momentum after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where:
- m₁, m₂ = masses of the two objects
- u₁, u₂ = velocities before the collision
- v₁, v₂ = velocities after the collision
Key points:
- Momentum is conserved in collisions and explosions
- The system must be isolated – no external forces like friction must act
- Momentum is a vector, so direction matters; use positive and negative values for opposite directions
- Kinetic energy is NOT always conserved (only in elastic collisions)
- Conservation of momentum applies to all interactions: collisions, explosions, and separations
Object A (mass 2 kg, velocity 5 m/s) collides with object B (mass 3 kg, initially at rest). After collision, A moves at 2 m/s. Find B's velocity. Before: (2 × 5) + (3 × 0) = 10 kg m/s. After: (2 × 2) + (3 × v₂) = 10. So 4 + 3v₂ = 10, giving v₂ = 2 m/s.
Always identify the system and define a positive direction at the start. Show that total momentum before equals total momentum after. Examiners will check your direction conventions and arithmetic carefully.
Section 5
How do we solve one-dimensional momentum problems?
Solving conservation of momentum problems requires a systematic approach:
- Define the system – identify which objects are involved
- Choose a positive direction – typically rightward or the initial direction of motion
- List initial data – write down all masses and velocities before the event
- Apply conservation – set total momentum before = total momentum after
- Solve algebraically – rearrange to find the unknown
- Check the answer – verify the result makes physical sense
Common scenarios:
| Scenario | Initial State | Final State |
|---|---|---|
| Collision | Two objects moving | Objects may stick or separate |
| Explosion | One object at rest | Objects move apart in opposite directions |
| Separation | Objects in contact | Objects move apart |
Important notes:
- In inelastic collisions, objects may stick together; total momentum is conserved but kinetic energy is lost
- In explosions, momentum is conserved even though the objects push apart; use opposite signs for velocities
- Always include units (kg m/s) and show working clearly
An explosion: a 6 kg object at rest explodes into two pieces. One piece (2 kg) moves left at 10 m/s. Find the velocity of the other piece (4 kg). Taking right as positive: before = 0 kg m/s. After: (4 × v) + (2 × −10) = 0. So 4v − 20 = 0, giving v = 5 m/s (to the right).
Must Know
- p = mv: Momentum equals mass times velocity, measured in kg m/s or N s
- Impulse = FΔt = Δ(mv): Force multiplied by time equals the change in momentum
- F = Δp/Δt: Resultant force is the rate of change of momentum; this is Newton's second law in its fundamental form
- Conservation of momentum: In an isolated system, total momentum before equals total momentum after (m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂)
- Momentum is a vector: Always include direction; use positive and negative values for opposite directions
- Closed systems have no external forces: Friction, air resistance, and applied external forces must be negligible for conservation to apply
That's the notes covered.
Carry on to the next subtopic.