A disk of mass M and radius R spins freely with angular velocity ωi about a fixed axis running through its center. A small piece of clay of mass m is dropped (direction: into the page as shown in the figure) at radius R/2 on the disk and sticks. (i) Taking the rotational axis of the disk to be the system axis, what is the total angular momentum of the disk-plus-putty before the collision? (ii) What is the final angular velocity ωf of the disk after the collision? (iii) What is the ratio of the final kinetic energy to the initial kinetic energy? (iv) What is the force of static friction holding the clay to the disk after the collision?

A disk of mass M and radius R spins freely with angular velocity ωi about a fixed axis running through its center. A small piece of clay of mass m is dropped (direction: into the page as shown in the figure) at radius R/2 on the disk and sticks. (i) Taking the rotational axis of the disk to be the system axis, what is the total angular momentum of the disk-plus-putty before the collision? (ii) What is the final angular velocity ωf of the disk after the collision? (iii) What is the ratio of the final kinetic energy to the initial kinetic energy? (iv) What is the force of static friction holding the clay to the disk after the collision?

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Question

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(i) Taking the rotational axis of the disk to be the system axis, what is the total angular momentum of the disk-plus-putty before the collision?

(ii) What is the final angular velocity ωf of the disk after the collision?
(iii) What is the ratio of the final kinetic energy to the initial kinetic energy?
(iv) What is the force of static friction holding the clay to the disk after the collision?

Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.

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