# Question #3e7ef

Jul 28, 2017

work done is zero as the displacement is zero.

#### Explanation:

Everytime an object completes a circle in uniform circular motion, the displacement of the object is zero as it returns to its starting position.And according to formula of work,

$W = F \cdot S$

where $S$ is zero for uniform cicular motion hece work done is zero.

Another reason is that the angular velocity($\omega$), Angular accelaration($\alpha$), centripetal acccelaration and tangential accelaration all are perpendicular to each other.Hence work done is zero as they have no components on each other.

Jul 28, 2017

I agree with the above, but think it can be explained more simply.

#### Explanation:

Imagine you are on a satellite orbiting the Earth, your velocity is a tangent to the orbit, the force causing you to remain in orbit (gravity) is at right angles to the velocity vector. Thus no work is done in the direction of the motion, as your displacement from the Earth is constant.

Work is better defined as

$W = F . s \cos \left(\theta\right)$

which reduces to zero when the angle between force and displacement is $90$ degrees.

If work was done in the direction of travel, your velocity would increase and you would move into a higher orbit.