Uniform Circular Motion
An object is in unform circular motion if it is moving in a circle at a constant velocity. For example, a dog running around a circular park at a constant velocity of 5 m/s would be travelling in Uniform Circular Motion.
An essential question to uniform circular motion: if an object is accelerating, does that always mean that it's speed is increasing? The answer is it depends. Because velocity is a vector, if velocity changes direction, then velocity is essentially changing, and any change in velocity is essentially an acceleration. Therefore, when an object moves in a circle, and is therefore constantly changing direction and velocity, their velocity is always changing. Anything moving in a circle accelerates in the direction towards the center of the circle (centripetal means "center seeking"). Centripetal acceleration can be found with the equation ac = v^2/r. For example, let say there is a car moving at 20 m/s around a circle with radius of five meters. Itl's centripetal acceleration would equal (20 m/s)^2/5m, or 80 m/s^2.
For an object moving in uniform circular motion, it's centripetal force is also always in the direction of the center of the circle. Centripetal force equals mass times centripetal acceleration. Because acceleration equals v^2/r, centripetal force can also be expressed as m(v^2/r).
Frequency and Period
Frequency, or "F," is the number of revolutions or cycles an object takes around a circle in one second. It is measured in Hertz (Hz). Period, or "T,", is the time it takes for an object to take one complete revolution or cycle, and is measured in seconds. So let's say our car. Period can also equal time divided by revolutions. For example, let's say a lawn mower is moving around a circular yard, and takes 1200 seconds to make 3 revolutions. It's period would equal 1200 seconds divided by 3 revolutions, or 400 seconds. F=1/T, and T=1/F, so if you have either frequency or period, you can always find the other. The frequency of the lawn mower would therefore be 1/400s, or .0025 Hertz.