In Uniform Circular Motion is the Angular Velocity constant? And is the Work done zer0?

Question

Why the work done in UCM is zero. And please specify the reason to first question also!

Answer 1

The angular velocity is constant for UCM by definition. That's what "unifom" means in this context. No work is done because there is no *net* force or torque on the object.

Answer 2

Yes to both.

In uniform circular motion R = const. and |v| = const., therefore angular velocity ω = |v|/R = const.

In uniform circular motion |v| = 0, therefore the tangential component of vector acceleration = 0. The vector acceleration a (and hence the force f = ma) is always perpendicular to the trajectory, thus the work applying on the motion is 0.

Answer 3

The angular velocity is constant.  The work done is 0 if the motion stops at the starting point only.  If the stopping point is any place else some work is done.  The amount done is only the weight by distance  away from the starting point, not the full 360 degrees for every rotation. (In other words if the you make 3 1/2 circuits only the the 1/2 circuit can be considered work.)

Answer 4

Yes,when the motion is uniform,the angular velocity is constant.

as we know,

     theta=l/r

or,theta/t = l/t *r

since r ie. radius is always constant.

theta/t ie. angular velocity is directly proportional to l/t ie. linear velocity.so, when linear velocity is constant,angular velocity is constant too.

we know,

  work done = F d cos theta

          since,the angle between the direction of force applied and the direction of displacement of object is 90 degrees,

                                                         cos theta = 0

      therefore,

       work done = 0