# Question #199e6

Nov 28, 2017

Because the motion is non-uniform.

#### Explanation:

Uniform motion is motion with constant velocity. Non-uniform circular motion would be circular motion whose angular velocity changes. With circular motion,

$\text{work" = "torque"*"angular displacement}$.

Assuming the body does not change shape or mass, if the angular velocity is changing, the kinetic energy of the rotating body is changing. Work is required to accomplish that.

I hope this helps,
Steve

Nov 28, 2017

There will be work done in no-uniform circular motion.

#### Explanation:

Work is a dot product, not a cross product, meaning that some component of the force vector and displacement vector need to be in the same direction in order for work to be non-zero. Consider the direction of each of this vectors in the case of uniform circular motion.

Picture a ball on a string that is spun around a center point. The centripetal force that keeps the ball moving in a circle is the tension on the string. This tensile force points toward the center of the circular motion. Now consider the direction of the motion of the ball. The ball is moving tangential to the circle. This is true at every point in the balls motion. Therefore, the two vectors will always be perpendicular. This means that the dot product, and thus work, will always be zero.

Now consider the case where the speed of the ball is increasing or decreasing. This would be non-uniform circular motion. The ball would need to have an additional acceleration vector, and by Newton's second law, an acceleration vector, with some component in the tangent direction. Since this is the same direction as the displacement vector, the work will necessarily be non-zero. 