Calculate momentum and force from momentum change
Use signed velocity to calculate momentum, then find mean force from the rate of momentum change.
Section 3 · Dynamics
AS Level · Cambridge International Physics 9702, 2025–2027 syllabus, Topic 3. These original explanations and practice support theory study; they do not establish supervised practical competence or replace timed assessment and teacher review. Drag is treated qualitatively, and coefficient of restitution is outside this syllabus section.
Before you begin
- Use vectors and signed values consistently, and distinguish mass from weight.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which expression defines linear momentum?
What you will learn
- Define and calculate linear momentum p = mv
- Use momentum direction and SI units
- Calculate mean force from change in momentum per unit time
Momentum keeps the direction of velocity
Linear momentum is the product of mass and velocity, p = mv. Mass is a scalar, so momentum points in the direction of velocity. In SI units its unit is kg m s⁻¹.
Choose a positive direction and use signed velocities for one-dimensional motion. A negative momentum indicates motion opposite to that chosen direction; it does not mean that the object's mass or speed is negative.
Force describes how quickly momentum changes
The resultant force is the rate of change of momentum: F = Δp/Δt. For a constant mass, this agrees with F = ma. A short interaction can still produce a substantial momentum change if the mean force is large.
Calculate Δp = p_final − p_initial using the same sign convention throughout. The equation gives the mean resultant force over the interval when the force is not constant. Its direction matches the momentum change.
Pause and explain
A force acts for a fixed time. What does its impulse correspond to in this topic?
Worked example
A 0.20 kg ball moves east at 5.0 m s⁻¹, then rebounds west at 3.0 m s⁻¹ in 0.040 s. Find its momentum change and mean force.
Show the worked solution
- Take east as positive: pᵢ = 0.20 × 5.0 = +1.0 kg m s⁻¹.
- The final velocity is −3.0 m s⁻¹, so p_f = −0.60 kg m s⁻¹ and Δp = −1.60 kg m s⁻¹.
- Mean force = Δp/Δt = −1.60/0.040 = −40 N.
Answer Momentum change 1.60 kg m s⁻¹ west; mean resultant force 40 N west.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the momentum of a 1.2 kg trolley moving at 4.0 m s⁻¹ north.
Give me a hint
Multiply mass by velocity and keep its direction.
Compare my reasoning
- Use p = mv.
- p = 1.2 × 4.0 = 4.8 kg m s⁻¹.
- Momentum points north with the velocity.
4.8 kg m s⁻¹ north.
Look for these in your work
- Definition used
- Magnitude calculated
- Direction and unit stated
A 0.50 kg ball changes velocity from +8.0 m s⁻¹ to −4.0 m s⁻¹ in 0.20 s. Find the mean resultant force.
Give me a hint
Calculate final momentum minus initial momentum; retain the signs.
Compare my reasoning
- pᵢ = 0.50 × 8.0 = +4.0 kg m s⁻¹.
- p_f = 0.50 × (−4.0) = −2.0 kg m s⁻¹, so Δp = −6.0 kg m s⁻¹.
- F = Δp/Δt = −6.0/0.20.
30 N in the negative direction.
Look for these in your work
- Signed momenta calculated
- Change is final minus initial
- Mean force direction and magnitude correct
A 1200 kg car slows from 20 m s⁻¹ to 14 m s⁻¹ in 3.0 s along a straight road. Find the mean resultant force on the car.
Give me a hint
Take the original travel direction as positive.
Compare my reasoning
- Δv = 14 − 20 = −6.0 m s⁻¹.
- Δp = mΔv = 1200 × (−6.0) = −7200 kg m s⁻¹.
- F = Δp/Δt = −7200/3.0.
2.4 × 10³ N opposite to the car's original direction.
Look for these in your work
- Direction convention stated
- Momentum change calculated
- Force sign interpreted
Common mistakes
- Ignoring the direction reversal when finding Δp
- Dividing by the wrong time interval
- Calling momentum change a scalar
What can you explain now?
Which expression defines linear momentum?
Compare with the explanation
p = mv
Momentum is mass multiplied by velocity.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why must the final momentum be subtracted from the initial momentum with signs?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.