Use mass, resultant force and Newton’s laws
Connect inertia to mass, apply F = ma to the resultant force, and identify the two bodies in a Newton’s third-law pair.
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
What does mass measure in this topic?
What you will learn
- Explain mass as resistance to a change in motion
- Use resultant force F = ma with acceleration in the force direction
- State and apply Newton’s three laws
Mass measures inertia
Inertia describes an object's resistance to a change in its velocity. For the same resultant force, a larger mass produces a smaller acceleration; mass is the measure of this resistance to change in motion.
A force diagram can help identify all forces on one chosen object. Add them as vectors to find the resultant. If that resultant is zero, the object has no acceleration: it remains at rest or moves at constant velocity.
Use Newton's laws on the correct object
Newton's first law describes motion when the resultant force is zero. Newton's second law for constant mass gives resultant force F = ma, so acceleration points in the same direction as the resultant force. Choose a positive direction before assigning signs.
Newton's third-law forces are equal in magnitude and opposite in direction, but act on different objects. They do not cancel in a force diagram for one object. Name both bodies and both forces to avoid pairing unrelated forces.
Pause and explain
A book pushes down on a table. Which force is its Newton's third-law partner?
Worked example
A 1.5 kg trolley experiences a resultant horizontal force of 6.0 N east. Find its acceleration.
Show the worked solution
- Use the resultant force, not one force in isolation: F = ma.
- Rearrange a = F/m = 6.0/1.5.
- The acceleration points east, in the same direction as the resultant force.
Answer 4.0 m s⁻² east.
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.
A 4.0 kg cart has a resultant force of 10 N to the right. Find its acceleration and explain how the direction follows.
Give me a hint
Use the net force in F = ma, then state its sign or direction.
Compare my reasoning
- Take right as positive; F = +10 N.
- a = F/m = 10/4.0.
- Acceleration has the same direction as the resultant force.
2.5 m s⁻² to the right.
Look for these in your work
- Resultant force selected
- F = ma rearranged correctly
- Acceleration direction stated
A 2.0 kg object accelerates at 3.0 m s⁻² west. Find the resultant force.
Give me a hint
The force and acceleration have the same direction.
Compare my reasoning
- Use F = ma.
- F = 2.0 × 3.0 = 6.0 N.
- Give the direction as west.
6.0 N west.
Look for these in your work
- Correct relationship used
- Magnitude calculated
- Direction matches acceleration
A swimmer pushes water backward. State the Newton's third-law partner and explain why it does not cancel the force on the swimmer.
Give me a hint
Name the agent and object for each force.
Compare my reasoning
- The swimmer exerts a backward force on the water.
- The water exerts an equal forward force on the swimmer.
- The paired forces act on different objects.
The water pushes forward on the swimmer with equal magnitude and opposite direction. It does not cancel the swimmer's force in the swimmer's force diagram because it acts on the swimmer while the original force acts on the water.
Look for these in your work
- Both bodies identified
- Equal and opposite directions stated
- Different objects explained
Common mistakes
- Using one force instead of the resultant
- Giving acceleration the opposite direction to the resultant
- Treating a third-law pair as forces on the same object
What can you explain now?
What does mass measure in this topic?
Compare with the explanation
Resistance to a change in motion
Mass is the measure of an object's inertia.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
How do you tell whether two forces form a Newton's third-law pair?
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.