A student sits on a rotating stool holding two 2.3-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.3-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 0.41 m from the rotation axis.

(a) Find the new angular speed of the student.

(b) Find the kinetic energy of the student before and after the objects are pulled in.
before J
after J

Explanation / Answer

This is the conservation of angular momentum
For the first part we can get L

L = Iw
L = 3*0.75 = 2.25

L = mr^2 w

2.25 = 4.6*.41^2 * w


w = 2.25/4.6/.41^2
w = 2.91 rad/s



b) kinetic energy = K = Iw2/2

Before: K = 3*.75^2 / 2 = .84375J

AFTER: K = mr2w2/2 = 4.6*.41^2 * 2.91^2 / 2 = 3.27J

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