You can see from the animation that to change the direction of a moving body, a force is applied at an angle to the motion. This is a change in the velocity's direction and is therefore an acceleration.

     Recall that postion, velocity, acceleration and force are all vectors. This means that each has direction and magnitude. If you change a velocity's direction OR magnitude then you have created an acceleration. In circular motion we are going to look at postion, velocity, acceleration and force. We will look at defining the direction and then the magnitude.

     The radius is the position or radius vector starts at the center and points to the body's location. (See the animation below.)

The velocity vector is tangent to the circle and is identified as the "tangential velocity." This makes it perpendicular to the radius vector. (See the animation below.)

The acceleration vector points to the center of the circle. Since it seeks the center of the circle it is identified as the "centripetal acceleration."(See the animation below.) [Any quantity pointing to the center of the circle is described with the adjective, "centripetal."]

The centripetal force is the force that also points to the center of the circle. It can be a vector that is drawn shorter, equal, or longer than the centripetal acceleration vector. (See the animation below.)

Time is a special measurement for circular motion. Because the motion repeats itself, the time comes in groups. For example, a ferriswheel spins once every 1/2 minute, (30 seconds.) If the ferriswheel spins for 5 minutes, then ferriswheel has spun 10 times or in 10 groups of 30 seconds. Each time-group is called a "period." A period of motion is the time to get back to the stating position. The repeating motion is called a "cycle." Therefore a period is defined as the time to complete one cycle of motion. Use a capital "T" to represent the period in math equations . [A lower case "t" is a generic variable for any amount of time. It is the wrong variable if you mean the period.]

Another term used to describe the relationship between time and the cycles is the frequency. The frequency is the defined as the number of cycles per second. Use a lower case "f" in the equations to represent frequency. [An upper case "F" stands for force, NOT frequency.]

If the ferris wheel spins with a period of 30 seconds then it will spin with a frequency of (1/30)Hz.

The period describes the time to complete a cycle of motion. It is measured in

However, a cycle is not a unit, so the period is just measured in the S.I. unit of seconds. It is calculted bu taking the time to complete a nmber of cycles and dividing it by the number of cycles.

Example

What is the period of merry-go-round that spins around 3 times in 90 seconds?

Solution

Frequency is the inverse of period. It is described as

It is measured in units of

However, the standard unit is named after Franc Hertx and instead is called a "Hertz." Abreviated as "Hz."