Explain the direction of centripetal acceleration
Relate a perpendicular inward force to changing velocity direction and uniform circular motion.
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 is the direction of centripetal acceleration?
What you will learn
- Explain why a perpendicular force produces centripetal acceleration
- Relate inward acceleration to circular motion at constant angular speed
- Distinguish constant speed from constant velocity
A centripetal acceleration points towards the centre
In circular motion the velocity is tangential to the path. The acceleration required to keep the path circular points towards the centre, perpendicular to the instantaneous velocity.
A force of constant magnitude that always acts perpendicular to the direction of motion continually changes the direction of velocity. If the speed and radius remain constant, it produces circular motion with constant angular speed.
Constant speed does not mean zero acceleration
In uniform circular motion, speed can stay constant while velocity changes because velocity includes direction. A changing velocity means acceleration is present even when its magnitude of speed does not change.
The inward force does no work in the ideal constant-speed model because it is perpendicular to the instantaneous displacement. It changes the direction, not the magnitude, of velocity.
Pause and explain
Can an object accelerate while its speed stays constant?
Worked example
A ball moves at constant speed around a horizontal circle on a string. State the direction of its acceleration and explain why it is not zero.
Show the worked solution
- The velocity is tangent to the circle at each point.
- The acceleration points toward the centre, perpendicular to velocity.
- Velocity direction changes continuously, so acceleration is non-zero even though speed is constant.
Answer Acceleration is radially inward; the velocity direction changes continuously.
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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 car travels at constant speed around a flat circular bend. State the direction of its acceleration and the role of the resultant force.
Give me a hint
The acceleration direction is the direction in which velocity is changing.
Compare my reasoning
- Velocity is tangent to the bend.
- Centripetal acceleration points to the centre of curvature.
- The resultant horizontal force must be inward to produce that acceleration.
The acceleration and resultant force are toward the centre of the bend.
Look for these in your work
- Velocity direction distinguished
- Acceleration directed inward
- Force role stated
Explain why a constant-magnitude force perpendicular to motion can cause circular motion without changing speed.
Give me a hint
A perpendicular force changes the perpendicular component of velocity.
Compare my reasoning
- The force is perpendicular to instantaneous velocity.
- It changes velocity direction rather than its magnitude.
- A constant inward acceleration maintains the circular path and constant angular speed under the stated conditions.
It continually turns the velocity inward while leaving speed unchanged, producing uniform circular motion under the stated conditions.
Look for these in your work
- Perpendicular geometry used
- Speed and direction separated
- Circular result explained
A student draws a centripetal-force arrow tangent to a circular path because the object is moving tangentially. Correct the diagram description.
Give me a hint
Separate the object's instantaneous velocity from the force causing its path to curve.
Compare my reasoning
- Velocity is tangent to the path.
- The resultant centripetal force is perpendicular to velocity and directed toward the centre.
- The tangent arrow represents velocity, not centripetal force.
Keep velocity tangent, but draw the resultant centripetal force radially inward toward the centre.
Look for these in your work
- Velocity direction retained
- Force direction corrected
- Vectors distinguished
Common mistakes
- Drawing centripetal acceleration tangent to the circle
- Claiming a constant speed means no acceleration
- Treating centripetal force as a new type of force rather than the inward resultant
What can you explain now?
What is the direction of centripetal acceleration?
Compare with the explanation
Towards the centre
It continually turns the velocity toward the circular path.
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Make it stick
How can velocity change when an object's speed is constant?
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