Calculate centripetal force
Use F = mrω² or F = mv²/r and identify the real inward resultant force.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 12. These original calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use radians, angular speed, velocity, acceleration, mass and resultant force with consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does F = mv²/r represent?
What you will learn
- Recall and use F = mrω²
- Recall and use F = mv²/r
- Identify the physical interaction providing the centripetal resultant
Resultant inward force produces circular acceleration
Newton's second law gives the centripetal resultant F = ma. Substituting either centripetal-acceleration expression gives F = mrω² or F = mv²/r.
These equations calculate the inward resultant, not a new type of force. Depending on the situation, tension, friction, gravity or a contact force may provide it. Identify the physical force and draw its direction toward the centre.
Check the conditions and units
Use mass in kilograms, radius in metres, speed in metres per second and angular speed in radians per second. The result is a force in newtons directed toward the centre.
If several real forces act radially, their vector resultant supplies the required centripetal force. Do not add a separate outward force to Newton's second-law equation in an inertial frame.
Pause and explain
A 2.0 kg mass moves at 3.0 m s⁻¹ on radius 1.5 m. Find inward resultant force.
Worked example
A 0.50 kg object moves at 6.0 m s⁻¹ in a circle of radius 3.0 m. Find the inward resultant force.
Show the worked solution
- F = mv²/r.
- F = 0.50 × 6.0²/3.0.
- State newtons toward the centre.
Answer F = 6.0 N inward.
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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 0.20 kg ball moves at 4.0 m s⁻¹ in a circle of radius 0.80 m. Find centripetal resultant force.
Give me a hint
Use F = mv²/r and retain the inward direction.
Compare my reasoning
- F = 0.20 × 4.0²/0.80.
- F = 0.20 × 20.
- State newtons toward the centre.
4.0 N inward.
Look for these in your work
- Mass included
- Speed squared
- Resultant direction stated
A 1.5 kg mass rotates at 5.0 rad s⁻¹ on radius 0.40 m. Find centripetal force.
Give me a hint
Use the angular-speed form F = mrω².
Compare my reasoning
- F = 1.5 × 0.40 × 5.0².
- F = 1.5 × 0.40 × 25.
- Give newtons inward.
15 N inward.
Look for these in your work
- Angular formula selected
- Substitution correct
- Force direction and unit stated
A car turns on a level road. State which physical interaction can provide the inward resultant and explain what happens if it is insufficient.
Give me a hint
Name the horizontal road force and compare its available magnitude with mv²/r.
Compare my reasoning
- Static friction between the tyres and road can provide inward force.
- The required resultant is mv²/r toward the curve's centre.
- If available friction is insufficient, the car cannot follow that radius at that speed and may skid outward relative to the curve.
Tyre-road friction supplies the centripetal resultant; if it is too small, the car skids and cannot maintain the circular path.
Look for these in your work
- Physical interaction identified
- Required force related
- Insufficient-force consequence explained
Common mistakes
- Calling centripetal force a separate interaction
- Using speed rather than speed squared
- Forgetting to identify which real force supplies the inward resultant
What can you explain now?
What does F = mv²/r represent?
Compare with the explanation
The inward resultant force for circular motion
It is the force required for the centripetal acceleration.
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Make it stick
Why should you name the real interaction that provides centripetal force in a situation?
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.