A flywheel is rotating initially with an angular velocity of 5.0 rad/s clockwise

Question

A flywheel is rotating initially with an angular velocity of 5.0 rad/s clockwise. Sometime later it is rotating with an angular velocity of 8.0 rad/s counterclockwise. At the later time, the wheel is at an angle of 4.0 rad counterclockwise relative to the initial orientation of the wheel. Assume uniform acceleration.

(a) What is the magnitude of the angular acceleration of the flywheel in rad/s2?
  rad/s2

(b) What is the direction of the angular acceleration?

Clockwise

Counterclockwise

(c) Relative to the initial position, what is the angle of the wheel when it momentarily comes to rest?
  rad

Explanation / Answer

here,

taking counterclockwise as +ve direction

initial angular speed , w0 = - 5 rad/s

final angular speed , w = 8 rad/s

theta = 4 rad

a)

let the angular accelration be alpha

w^2 - w0^2 = 2 * alpha * theta

8^2 - 5^2 = 2 * alpha * 4

alpha = 4.87 rad/s^2

b)

as the angular accelration is positive

the direction is counterclockwise

c)

let the angle be theta'

w^2 - w0^2 = 2 * alpha * theta'

for the wheel to come to stop , w = 0

0 - (-5)^2 = 2 * 4.87 * theta'

theta' = 2.56 rad

the angle of the wheel when it momentarily comes to rest is 2.56 rad

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