Question

A uniform disk of mass M and radius R is initially rotating freely about its central axis with an angular speed of ω, and a piece of clay of mass m is thrown toward the rim of the disk with a velocity v, tangent to the rim of the disk as shown. The clay sticks to the rim of the disk, and the disk stops rotating.

33. What is the magnitude of the total angular momentum of the clay-disk system before the clay sticks to the disk?

A) 1 2 MR2 ω − mvR

B) 1 2 MR2 ω − mv

C) 1 2 MR2 ω + mvR

D) mvR

E) 1 2 MR2 ω

34. What is ω in terms of the other variables given?

A) 2mv MR

B) Mv mR

C) v R

D) mv MR

E) 2Mv mR

35. If the disk is replaced by a hoop of mass M and radius R with the same initial conditions, does the hoop rotate clockwise, counterclockwise, or stop rotating after the collision?

A) Stops rotating

B) Rotates clockwise

C) Rotates counterclockwise

D) Not enough information is given.

Answer 1

33)
A) (1/2)*M*R^2*w - m*v*R

Lin = Lf

L_disk + L_person = 0

(1/2)*M*R^2*w - m*v*R = 0

so, Li = (1/2)*M*R^2*w - m*v*R

34)
A) 2*m*v/(M*R)

(1/2)*M*R^2*w - m*v*R = 0

(1/2)*M*R^2*w = m*v*R

w = 2*m*v/(M*R)

35)

The hoop will continue in the same direction. (I cant tell you the direction because figure is not given)

Initially if it is rotating clockwise, in continues in clockwise direction.

Initially if it is rotating counter clockwise, in continues in counter clockwise direction.