A student sits on a rotating stool holding two 3.4-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.45 m from the rotation axis.

Question

(a) Find the new angular speed of the student. (rad/s)
(b) Find the kinetic energy of the student before and after the objects are pulled in.
-before(J)
-after(J)

Answer 1

Use conservation of momentum

Initial momentum:

The momentum of inertia of the objects the students is m*r^2

(3.0 + 3.4*1^2 + 3.4*1^2)*wi = (3.0 + 3.4*.45^2 + 3.4*.45^2)*wf

where wi = 0.75 is the initial angular momentum, and wf is the final angular momentum. Solve for wf

b) Kinetic energy = 1/2*I*w^2

Initial kinetic energy is

(3.0 + 3.4*1^2 + 3.4*1^2)*wi^2

Final kinetic energy is

(3.0 + 3.4*.45^2 + 3.4*.45^2)*wf^2

Answer 2

forgot the 1/2 in the last 2 parts