Uniform circular motion

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

Question: Is there an acceleration in uniform circular motion?

  1. Yes
  2. 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 ac that points radially inward and keeps a particle on a circular path.

The centripetal acceleration is ac=v2/r   (radially inward)

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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: at = 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 at = 0, while ac is non-zero and points in the radial direction.