A student sits on a rotating stool holding two 2.3-kg objects. When his arms are
ID: 1348488 • Letter: A
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 0.38 m from the rotation axis.
(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.
Explanation / Answer
a)
MI = 3 + 2 * 2.3 = 7.6
L = 7.6 * 0.75
New MI = 3 + 4.6 * 0.5^2 = 4.15
New "w" = 7.6 * 0.75 / 4.15 = 1.37 rad/s
b)
KE before = 0.5 * 7.6 * 0.75^2 = 2.1375 J
KE after = 0.5 * 4.15 * 1.37^2 = 3.89 J
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