Example

Example (Centripetal Force)

We realized the speed of the motion in a circular path is proportional to the radius of the path.

This relationship can be given by the following equation. Also, we recognized, all the movements in circular paths are supported by a force towards the center of the circle.

Such a force is known as 'Centripetal Force' and mathematically presented by the following equation let's try to apply this result to understand this concept more clearly.

**Problem**
Imagine a 95-kg football player makes a turn on the football field. The player sweeps out a path that is a portion of a circle with a radius of 12-meters. He makes a quarter of a turn around the circle in 2.1 seconds. Determine the speed, the centripetal force acting upon the halfback.

If the player completes a quarter of a circle in 2.1 seconds, the time to complete a full circle will be 2.1*4 = 8.4seconds. The radius of the circle is R = 12 meters

Then, the speed of the circle should be;

And the centripetal forcce is given by,

We can use this result to learn more about the physics of taking turns. The above force you calculated as the centripetal force is required if the player want to take the turn at the speed he is moving. Usually this amount of force is given by the friction of the ground. So what happens is that the player who tries to take the bend while moving fast incline his body towards the center of the circle and try to push the ground away from the center.



Then the reaction force to his is exerted by the ground on the player.

This reaction force is produced by earth due to the friction.

The shoes of football players are made with knobs in order to increase the friction on the type of surfaces the game is played.

In dry days the contact between the earth and player is readilly producing the frictional force and therefore sharp movements are possible to observe.

But in wet days, the water on the surface ruduces the frictional force, therfore when pushing the ground with inclined bodies players are likely to slip off the path they are trying to make.