a) A uniform disk is constrained to rotate about an axis passing through its cen

Question

a) A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. If the disk starts from rest and is then brought in contact with a spinning rubber wheel, we observe that the disk gradually begins to rotate too. If after 30 s of contact with this spinning rubber wheel, the disk has an angular velocity of 3.0 rad/s, find the average angular acceleration that the disk experiences. (Assume the positive direction is in the initial direction of rotation of the disk. Indicate the direction with the sign of your answer.)

b) Assume after 30 s of contact with this spinning rubber wheel, the disk has an angular velocity of 11.0 rad/s. Once reaching this angular velocity, the wheel is moved away from the disk and the disk is allowed to continue to spin freely without friction about its axle. Find the angular distance that a fixed point on the rim of the wheel will travel in 30 s under these conditions.

Explanation / Answer

a) angular acceleration = (w2 - w1) / t

= (3.0 - 0) / (30)

average angular acceleration = 0.1 rad/s2

b) angular distance = w t

= 11 * 30

= 330 rad

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