# Circular Motion and Centripetal Force

Circular motion is caused by an unbalanced force acting towards the center of the circle. This force is called the centripetal  force which needs to be provided by a physical mechanism. e.g. gravity, friction, tension etc.

In a time △t, mass (m) moves from position (1) to position (2). The length of the line or arc between (1) and (2) will be the radius x △Ø. Therefore, △Ø = arc (1) -(2) / radius.

To work out the change of velocity from V2 to V1, △V = V2-V1. △V points towards the center of the circle. From doing numerous substitutions which are too completely and time consuming to type out, we can come to the following equation:

a = V² / r

Where a is the centripetal acceleration towards the center of a circle, V is velocity and r is the radius. From this equation, because we already know that F = ma…

F = mV² / r

Which is the equation for the centripetal force required. From this equation, we can produce a rough graph.

From the graph, the constant in the equation is the centripetal force / mass.

## Summary

• The centripetal force causes circular motion which is an unbalanced force that acts inwards towards the center of the circle.
• The acceleration from the centripetal force towards the center of the circle is V² / radius.
• The centripetal force requried for circular motion is mV² / radius.