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.
