Uniform circular motion has constant speed but changing velocity direction. Its acceleration is inward with magnitude a=rv2. One revolution covers 2πr, so v=T2πr, where T is period. Frequency is T1. At fixed radius, doubling speed quadruples acceleration; at fixed speed, doubling radius halves it.
The required inward resultant is F=rmv2. Tension, friction, gravity or a normal force can supply it. Do not add a separate centripetal force to a diagram already showing the actual interactions. If the inward constraint disappears, motion is initially tangential. For repeated turns, period equals total elapsed time divided by the number of revolutions.
Example 1
An object moves at 6.00ms−1 around a 2.00m radius circle. Find acceleration.
a=rv2=2.006.002=18.0ms−2 inward.
Example 2
A 0.500kg object has the same motion. Find inward resultant force.
Fnet =ma=0.500×18.0=9.00N toward the centre.
Watch out: Acceleration measures velocity change; the direction changes continuously in circular motion even at constant speed.