Rotational Motion?

Question

This question is really frustrating me. I would really appreciate help. Thanks!
A flywheel turns through 52 rev as it slows from an angular speed of 2.6 rad/s to a stop
(a) Assuming a constant angular acceleration, find the time for it to come to rest.
(b) What is its angular acceleration?
(c) How much time is required for it to complete the first 26 of the 52 revolutions?

Also, if you could show your work, that would be great. Thanks.

Answer 1

This is rotational kinematics. The equations you need are

2 α ( θ - θo ) = ω^2 - ωo^2
θ - θo = ωo t + 1/2 α t^2

α is the angular acceleration ( what you're looking for )

θ - θo is the angular displacement ( 52 revs or ( 2π ) ( 52 ) radians )

ω is the final angular velocity ( zero )

ωo is the initial angular velocity ( 2.6 rad / s )

t is the elapsed time.

Use the first equation to find the angular acceleration α, then use that value in the second equation to find the total elapsed time. The answer to part (c) is also found using the second equation (plug in the new angular displacement and solve for time).