This picture is an example of Uniform Circular motion. The object you see, the tie, is moving with the fan in a circle. The tie is moving around the circumference the fan, as it spins. The amount of full revolution the tie makes in a certain amount of time is called the frequency. The frequency is measured in Hertz.
To find the frequency, at which the tie spins, you have to divide the amount or revolutions by the amount of time it took to complete set amount of revolutions.
The tie does not have a constant velocity because it is continuously changing direction, so the tie is accelerating. This type of acceleration is called centripetal acceleration. The tie stays tangential to the circle formed as the fan spins.
To find the centripetal acceleration you must find the velocity, at which the tie spins around the circle, and divide that by the radius of the circle that is made as the fan spins.
The inward force that keeps the fan spinning and the tie, moving in a circle, is called the centripetal force. Without the centripetal force circular motion cannot occur, but it is not a specific type of force, in fact it is provided by the force that keeps the object tie in the circle. The centripetal force requirement is the force that keeps the tie moving in a circle. In this case it is a tension force that keeps the tie and the fan blades from flying off.
