Two wheels with identical moments of inertia are rotating about the same axle.The first is rotating clockwise at 2.0 rad/s,and the second is rotating counterclockwise at 6.0 rad/s.If the two wheels are brought into contact so that they rotate together,their final angular velocity will be
A)2.0 rad/s,counterclockwise.
B)3.0 rad/s,clockwise.
C)4.0 rad/s,counterclockwise.
D)5.0 rad/s,clockwise.
E)6.0 rad/s,clockwise.

Question

Quizplus · Accepted Answer

Since the moments of inertia are identical and the two wheels are rotating in opposite directions, their angular momenta are equal but opposite (L1 = - L2). When they are brought into contact, the two wheels act as a single system, with no external torques acting on them. Therefore, the total angular momentum of the system is conserved (Ltotal = L1 + L2). Initially, Ltotal = - I1 * 2.0 - I2 * (- 6.0) = - 2(I1 + I2) rad/s. Finally, when the two wheels rotate together, they have a common angular velocity w, and their total angular momentum is - (I1 + I2) * w. Therefore, - 2(I1 + I2) = - (I1 + I2) * w, which gives w = 2.0 rad/s counterclockwise (since the initial angular momentum is clockwise and the final angular momentum is counterclockwise). Therefore, the answer is C, 4.0 rad/s counterclockwise.

Two Wheels with Identical Moments of Inertia Are Rotating About