Angular Speed?

Question

A wheel turns through 5 revolutions while being accelerated from rest at 19 rpm/s.

What is the final angular speed?

How long does it take to turn the 5 revolutions?

Please Help. Do not know how to get started.

Answer 1

The equations for constant angular acceleration exactly parallel those for linear acceleration:

Wf = Wi + A x T
R = Wi x T + (1/2) x A x T^2

That is, the final angular velocity is a linear function of the initial angular velocity Wi, the angular acceleration A, and the time interval T.

The total rotation is linear in Wi and quadratic in T.

You know the total rotation (5 revolutions), the initial angular velocity (i.e. 0), and the angular acceleration, so you can solve the quadratic to compute T.

Using T you can use the velocity equation to compute Wf.

Just be careful in the computation because A is in rpm/s. You'll have to convert to revolutions/s^2 or revolutions/m^2 to get the right answer. Whichever you choose, use the same time units for the velocity.