A student sits on a rotating stool holding two 2.1-kg objects. When his arms are
ID: 1400222 • Letter: A
Question
A student sits on a rotating stool holding two 2.1-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 0.47 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
m = mass of each object = 2.1 kg
r = distance of objects from axis of rotation = 1 m
Ioi = moment of inertia of each object initially = m r2 = 2.1 (1)2 = 2.1
Iof = moment of inertia of each object finally = m r2 = 2.1 (0.47)2 = 0.464
I = moment of inertia of student plus stool = 3 kg m2
wo = initial angular speed = 0.75 rad/s
w = final angular speed
using Conservation of angular momentum :;
(I + 2Ioi) wo = (I + 2Iof )w
(3 + 2 (2.1)) (0.75) = (3 + 2(0.464)) w
w = 1.375 rad/s
b)
KE of student before = (0.5) (I + 2 Ioi ) wo2 = (0.5) (3 + 2 (2.1)) (0.75)2 = 2.025 J
KE of student finally = (0.5) (I + 2Iof )w2 = (0.5) (3 + 2(0.464)) (1.375)2 = 3.71 J
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