Uniform circular motion
In circular motion at constant angular speed , , so circular motion requires a centripetal force towards the origin.
Example 3.1 (Circular Motion at Constant Angular Speed)
Radial and tangential components
In polar coordinates the acceleration is
With constant, so that , and constant angular speed with , only the radial term survives:
The acceleration points towards the origin, and by Newton’s second law a force of magnitude towards the origin is required.
Related
Stated in
- Example 3.1 (Circular Motion at Constant Angular Speed)§3.2 Polar Coordinates in the Plane