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# Conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationships that exist

**Centripetal force : **a force which acts on a body moving in a circular path and is directed towards the centre around which the body is moving.

**Radius : **the radius of the circular path in which motion is taking place

**Speed ** : The uniform is speed with which the object is moving in the circular path

**NOTE:** although the speed in uniform circular motion is constant, the velocity is changing.

Setup an experiment to measure the centripetal force in uniform circular motion by varying the mass, speed and radius one at a time and plotting the graph.

You would require a conical pendulum , of variable length (*l*) to be able to measure the period (T) of motion and radius (*r*) of circular motion (r)

Background calculations

From the free body diagram on the right we can see that :

Then the centripetal force is

So:

To check relationships between variables:

- we can see from calculation of Centripetal force itself that
- Now we can vary the velocity of the circular motion and calculate the centripetal force
- to measure velocity we use the formula , where
*r*is the radius of the circular motion and T is the time period - while varying the velocity keep the radius constant by changing the length of the pendulum
- measure Time period and radius and calculate the velocity . measure the mass and calculate the centripetal force
- Upon drawing the graph of F vs
*v*you will notice that

- to measure velocity we use the formula , where

- Now we can vary the radius of the circular motion and calculate the centripetal force
- while varying the radius keep the velocity constant by changing the length of the pendulum such that the ratio is constant.
- measure the radius. Then measure the mass and calculate the centripetal force
- Upon drawing the graph of F vs
*r*you will notice that

Hence we can conclude that centripetal force required for uniform circular motion is

Extract from *Physics Stage 6 Syllabus © 2017 *NSW Education Standards Authority (NESA)