Why Circular Motion Accelerates
Same speed, different velocity
- is motion around a circle at constant speed and constant radius.
- Velocity is a . It has a and a direction. The magnitude of velocity is speed.
- The velocity always points along the to the circular path.
An object moves once around a circle at constant speed. State what happens to the magnitude and direction of its velocity.
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The magnitude stays constant. The direction changes at every point on the path.
The inward change in velocity
- Acceleration is the change in velocity divided by the time taken.
- To find , move the two velocity arrows so that they start at one point. Do not change their lengths or directions.
- The change in velocity is the arrow from the end of to the end of .
- The change in velocity points towards the centre. The acceleration must point in the same direction.
- This inward acceleration is called .
Constant speed does not mean constant velocity. A change in direction is a change in velocity.
Force at 90° to the motion
- Centripetal acceleration is to the velocity.
- A points in the same direction as the acceleration.
- The inward force is at 90° to the velocity. It changes the direction of the velocity, not its magnitude, so the speed stays constant.
- Constant speed and constant radius give constant angular speed.
A force with constant size acts at 90° to the motion. It causes inward acceleration. The object then moves in a circle at constant speed.
Why the kinetic energy stays constant
The inward force does no work because the object does not move in the force direction. Its kinetic energy and speed therefore stay constant.
In terms of velocity and acceleration, describe uniform circular motion.
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The magnitudes of velocity and acceleration are constant. The velocity is always perpendicular to the acceleration.
An object moves in a circle at constant speed. State two quantities that change.
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Accepted answers include velocity, momentum, acceleration, resultant force and angular displacement. State any two.
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