What is the Work Done in Circular Motion?

[songoku]

Homework Statement

A body of mass m moves at constant angular speed $$\omega$$ in a horizontal circle of radius r. What is the work done on the body in one revolution?

a. zero

b. $$2\pi mr^2\omega ^2$$

c. $$\pi mr^3\omega ^3$$

d. $$mr^2 \omega ^2$$

e. $$mr^2 \omega ^2 /2$$

Homework Equations

W=F.s

The Attempt at a Solution

Because the displacement is zero, then the work done is zero?

Thanks

 

[Doc Al]

What direction is the force on the body? What direction does the body move?

Or: Consider the change in the body's kinetic energy.

 

[Fightfish]

Yup. Another way to see it is that the centripetal force does not change the energy of the body.

 

[theJorge551]

Yes. You must look at the directions of the centripetal force, and the direction of velocity, and you find your answer.

 

[songoku]

Hi all

The direction of centripetal force is towards the center of circle and direction of motion is tangential to the circle.
So, it means that the work done is always zero because the force is perpendicular to the direction of motion?

Thanks

 

[Doc Al]

The direction of centripetal force is towards the center of circle and direction of motion is tangential to the circle.
So, it means that the work done is always zero because the force is perpendicular to the direction of motion?

Right!