A flywheel is rotating initially with an angular velocity of 4.0 rad/s clockwise

Question

A flywheel is rotating initially with an angular velocity of 4.0 rad/s clockwise. Sometime later it is rotating with an angular velocity of 7.0 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/s^2? rad/s^2 (b) What is the direction of the angular acceleration? (c) Relative to the initial position, what is the angle of the wheel when it momentarily comes to rest?

Explanation / Answer

Here,

initial angular speed , wi = -4 rad/s

final angular speed , wf = 7 rad/s

theta = 4 radian

a) let the angular acceleration is a

Using third equation of motion

wf^2 - wi^2 = 2 * a * theta

7^2 - 4^2 = 2 * a * 4

solving for theta = 4.13 rad/s^2

the magnitude of angular acceleration of the flywheel is 4.13 rad/s^2

b)

the direction of angular acceleration is counter clockwise

c)

when it comes to rest , for the final angle

0 - 4^2 = 2 * theta * 4.13

theta = 1.94 rad

the angle of wheel is 1.94 radian clockwise from the initial position

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