Definition: Uniform circular motion is in a circular path at constant speed.
Question: Is there an acceleration in uniform circular motion?
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.
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.
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)
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.