Uniform circular motion: motion in a circular path at constant speed.

Is there an acceleration involved here?

1. Yes
2. No

Yes - the velocity changes because its direction changes.

Basic definitions

r = the radius of the circular path

T = the period, the time to go around once

v

=

2π r T

As in straight-line motion, the relationship between a and v is the same as that between v and r:

a

=

2π v T

Combining these two equations gives us:

centripetal acceleration:

ac

=

v2 r

Angular variables

For motion on circular paths it can be useful to describe motion using angular variables. Instead of asking how much distance has been covered, we sometimes ask how much of an angle something has spun through. There are equivalent questions for velocity and acceleration.

Distance: s = rθ

Velocity: v = rω

Acceleration: a_t = rα

This acceleration involves a speeding up or slowing down of an object as it moves along a circular path, and is equal to zero for uniform circular motion. The a is in a direction tangent to the circle, so its the tangential acceleration. This is very different from the centripetal acceleration, which acts in the radial direction.