U3AOS1 Topic 3: Circular Motion

The distance around a circle is the circumference and is calculated through the following formula

\[ d = \text{circumference} = 2 \pi r \]

Therefore the average speed can be calculated by dividing the distance around the circle by the time it takes

\[ \text{speed}_{avg} = \frac{d}{t} = \frac{2 \pi r}{t} \]

The average velocity will always be 0 since the object returns to its original position (no displacement). However, there is a varying instantaneous velocity since the direction is changing.

The acceleration is calculated through the following formula

\[ a = \frac{v^2}{r} = \frac{4 \pi^2 r}{T} \]

The acceleration always points toward the center of the circle. So the net force is always toward the center of the circle as well.

Using these equations, the force on a mass travelling in circular motion can be calculated by using Newton's Laws.

\[ F_{net} = ma = \frac{mv^2}{r} = \frac{4m \pi^2 r}{T} \]

A key note about circular motion is that the acceleration and the velocity are $ 90$ degrees out of phase. This means that if the velocity at $t = 0$ is to the right then the acceleration would be either up or down depending on the direction it is travelling in. This can be seen in the simulation below.