What you'll learn
This revision guide covers how momentum changes when forces act on objects, and introduces the concept of impulse. You'll learn to calculate momentum changes, understand the relationship between force, time and momentum, and apply these principles to safety features and collisions. These topics appear regularly in AQA GCSE Physics papers, particularly in calculations and extended response questions.
Key terms and definitions
Momentum — the product of an object's mass and velocity, measured in kilogram metres per second (kg m/s)
Impulse — the product of force and the time for which it acts, equal to the change in momentum, measured in newton-seconds (N s)
Conservation of momentum — the principle that the total momentum before an event equals the total momentum after, in a closed system
Collision — an event where two or more objects exert forces on each other for a relatively short time
Resultant force — the overall force acting on an object when all forces are combined
Rate of change — how quickly a quantity varies with respect to time
Core concepts
Calculating momentum
Momentum is calculated using the equation:
momentum = mass × velocity
p = m v
Where:
- p = momentum in kg m/s
- m = mass in kg
- v = velocity in m/s
Key points about momentum:
- Momentum is a vector quantity — it has both magnitude and direction
- The direction of momentum is the same as the direction of velocity
- A stationary object has zero momentum (v = 0)
- Doubling the velocity doubles the momentum
- Doubling the mass also doubles the momentum
For example, a car of mass 1200 kg travelling at 15 m/s has momentum: p = 1200 × 15 = 18,000 kg m/s in the direction of travel
Changes in momentum
When a force acts on an object, it causes the object's velocity to change, which means its momentum changes.
The change in momentum is calculated by:
change in momentum = final momentum − initial momentum
Δp = m v − m u
Where:
- Δp = change in momentum in kg m/s
- u = initial velocity in m/s
- v = final velocity in m/s
Important considerations:
- If an object speeds up, the change in momentum is positive
- If an object slows down, the change in momentum is negative
- Direction matters — use positive and negative values to represent opposite directions
- For objects starting from rest, u = 0, so Δp = m v
Force and rate of change of momentum
Newton's second law can be expressed in terms of momentum:
The resultant force acting on an object equals the rate of change of its momentum
This gives us the equation:
force = change in momentum ÷ time taken
F = (m v − m u) ÷ t
Or rearranged:
F = Δp ÷ t
Where:
- F = resultant force in N
- t = time in s
This equation shows that:
- A larger force produces a greater change in momentum in the same time
- The same change in momentum can be achieved with a smaller force acting for longer
- A shorter collision time means larger forces are involved
Impulse and the impulse-momentum relationship
Impulse is defined as force multiplied by the time for which the force acts:
impulse = force × time
F t = Δp
This leads to the impulse-momentum theorem:
The impulse acting on an object equals its change in momentum
This relationship is crucial for understanding:
- Why airbags and crumple zones increase safety
- How forces in collisions can be reduced
- The effect of follow-through in sports
The units for impulse are newton-seconds (N s), which are equivalent to kg m/s (the units of momentum).
Safety applications
Understanding momentum changes helps explain how safety features work by increasing the time over which momentum changes, thus reducing the force experienced.
Crumple zones in vehicles:
- Designed to collapse gradually during a collision
- Increase the collision time
- Reduce the force on passengers (F = Δp ÷ t — larger t means smaller F)
- The momentum change is the same, but it happens over a longer time
Airbags:
- Inflate rapidly during a collision
- Increase the time for the passenger to stop
- Spread the force over a larger area
- Reduce peak forces on the body
Seat belts:
- Stretch slightly during impact
- Increase stopping time compared to hitting a rigid surface
- Prevent passengers from continuing forward at the vehicle's original velocity
- Spread force across stronger parts of the body (chest and pelvis)
Crash mats and padding in sports:
- Increase the time taken to stop
- Reduce impact forces on athletes
- Same principle applies to gym mats, helmets, and protective equipment
Conservation of momentum in collisions
In a closed system (where no external forces act), the total momentum before a collision equals the total momentum after:
total momentum before = total momentum after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Where subscripts 1 and 2 refer to the two objects involved.
Types of collisions:
Elastic collisions — objects bounce apart; kinetic energy is conserved (not required in detail at GCSE)
Inelastic collisions — objects may stick together or crumple; some kinetic energy is converted to other forms
When objects stick together after collision:
- They have the same final velocity (v)
- Use: m₁u₁ + m₂u₂ = (m₁ + m₂)v
Direction is crucial:
- Choose a positive direction (usually right or forward)
- Velocities in the opposite direction are negative
- The sum must account for these signs
Worked examples
Example 1: Calculating momentum change
Question: A tennis ball of mass 58 g is hit by a racket. It approaches the racket at 12 m/s and leaves at 24 m/s in the opposite direction. Calculate the change in momentum of the ball. [3 marks]
Solution:
First, convert mass to kg: 58 g = 0.058 kg [1 mark]
Choose a direction as positive. Taking the initial direction as positive:
- Initial velocity, u = +12 m/s
- Final velocity, v = −24 m/s (opposite direction)
Initial momentum = m u = 0.058 × 12 = 0.696 kg m/s
Final momentum = m v = 0.058 × (−24) = −1.392 kg m/s [1 mark]
Change in momentum = final − initial = −1.392 − 0.696 = −2.088 kg m/s (or 2.1 kg m/s in the opposite direction) [1 mark]
Example 2: Force and time in collisions
Question: A car of mass 1500 kg crashes into a wall and comes to rest. Before the collision, the car was travelling at 8.0 m/s. The collision lasts 0.50 s. Calculate the average force exerted on the car during the collision. [4 marks]
Solution:
Initial velocity, u = 8.0 m/s Final velocity, v = 0 m/s (comes to rest) Mass, m = 1500 kg Time, t = 0.50 s
Change in momentum = m v − m u = (1500 × 0) − (1500 × 8.0) [1 mark] = 0 − 12,000 = −12,000 kg m/s [1 mark]
Force = change in momentum ÷ time [1 mark] F = −12,000 ÷ 0.50 F = −24,000 N
The average force is 24,000 N (or 24 kN) acting in the opposite direction to the car's motion [1 mark]
Example 3: Conservation of momentum
Question: A railway truck of mass 8000 kg moving at 3.0 m/s collides with a stationary truck of mass 6000 kg. After the collision, the trucks couple together and move off at the same velocity. Calculate their velocity after the collision. [4 marks]
Solution:
Before collision:
- Truck 1: m₁ = 8000 kg, u₁ = 3.0 m/s
- Truck 2: m₂ = 6000 kg, u₂ = 0 m/s
Total momentum before = m₁u₁ + m₂u₂ [1 mark] = (8000 × 3.0) + (6000 × 0) = 24,000 + 0 = 24,000 kg m/s [1 mark]
After collision:
- Combined mass = 8000 + 6000 = 14,000 kg
- Both trucks move at velocity v
Total momentum after = (m₁ + m₂)v = 14,000v
By conservation of momentum: 24,000 = 14,000v [1 mark]
v = 24,000 ÷ 14,000 = 1.71 m/s (or 1.7 m/s to 2 s.f.) [1 mark]
Common mistakes and how to avoid them
Forgetting to convert units — always convert grams to kilograms and ensure velocity is in m/s. Check that your final answer uses standard units (kg m/s for momentum, N for force)
Ignoring direction in momentum calculations — momentum is a vector. Use positive and negative signs consistently. If an object reverses direction, its final velocity has the opposite sign to its initial velocity
Confusing force with momentum — force causes momentum to change; it is not the same as momentum. Remember: F = Δp ÷ t, not F = p
Incorrectly applying conservation of momentum — only apply this when no external forces act. In collisions, internal forces between objects cancel out, but external forces (like friction) prevent conservation if significant
Mixing up impulse and momentum — impulse equals the change in momentum (F t = Δp), not momentum itself. Impulse is what causes momentum to change
Not showing your working — in calculations worth 3-4 marks, you must show each step. Writing only the final answer may only earn 1 mark even if correct
Exam technique for "Changes in momentum and force (impulse)"
Command word "Calculate" requires you to show all working and arrive at a numerical answer with correct units. Typically worth 3-4 marks: 1 for correct formula/method, 1-2 for substitution and working, 1 for correct answer with unit
Command word "Explain" requires you to apply physics principles to a context. For safety features, you must link increased collision time to reduced force using F = Δp ÷ t. Quality of written communication may be assessed
Watch for required significant figures or decimal places — the question may specify how to express your answer. If not specified, match the lowest number of significant figures in the question data
Extended response questions on momentum often require you to explain safety features. Structure your answer: state the momentum change is the same, explain how the feature increases time, conclude that force is reduced because F = Δp ÷ t, and link to reduced injury
Quick revision summary
Momentum equals mass times velocity (p = m v) and is measured in kg m/s. When forces act, momentum changes according to F = Δp ÷ t. Impulse (force × time) equals the change in momentum. Safety features like airbags and crumple zones increase collision time, reducing the force experienced. In collisions with no external forces, total momentum is conserved. Always include direction when working with momentum, as it is a vector quantity.