### Uniform circular motion

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

Question: Is there an acceleration in uniform circular motion?

- Yes
- No

Answer: Yes!! The velocity changes because direction changes. However
the speed remains constant.

Question: A ball is whirled in a circle. If the string is released when
the ball is at the position shown, which path will the ball follow?

Answer: If the string is released there is no force to deflect the path of
the ball, so it will continue in a straight line, following path 2.

### Basic Quantities in Circular Motion

r = the radius of the circular path

T = the period, the time to go around once

v = the *linear* velocity

a = the *linear* acceleration

The first 3 quantities are related by: v T = 2πr.

### Centripetal Acceleration

The crucial feature of uniform circular motion is centripetal acceleration a_{c} that points
radially inward and keeps a particle on a
circular path.

The centripetal acceleration is a_{c}=v^{2}/r (radially
inward)

(see transparency)

### Angular and Linear Variables

Circular motion is more usefully described using
angular variables. Instead of the distance covered, we focus on the
rotation angle. These angular variables are:

Distance: s = rθ θ = angular
position

Velocity: v = rω ω = angular velocity

Acceleration: a_{t} = rα; α = angular (tangential) acceleration

The tangential acceleration involves a speeding up or slowing down of an
object as it moves along a circular path,

Important: In uniform circular motion
a_{t} = 0, while a_{c} is non-zero and points in the radial
direction.