A flywheel is rotating initially with an angular velocity of 3.0 rad/s clockwise

Question

A flywheel is rotating initially with an angular velocity of 3.0 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 2.0 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? Counterclockwise Clockwise

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

Explanation / Answer

(a)

the angular acceleration is calculated as follows:

    alpha = wf^2 - w^2 /2*theta

             = ((7)^2 - (-3)^2)/2*2

            = 10 rad/s^2

b.

since the angular acceleration has positive sign, the

angular acceleration is directed in counterclockwise.

c.

the angle is calculated as follows:

   theta = wf^2 - w^2 /2* alpha

            = 0 - (3)^2 /2* 10

            = -0.45 rad

            = 0.45 rad, clockwise

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