A student sits on a rotating stool holding two 3.1-kg objects. When his arms are
ID: 1475616 • Letter: A
Question
A student sits on a rotating stool holding two 3.1-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 0.32 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.
before ______ (J) after ________ (J)Explanation / Answer
(A) Find the new angular speed of the student.
in rad/s
Angular momentum before = angular momentum after
Angular momentum before
Inertia of student plus stool = 3.0 kg-m^2
Inertia of weights = mr^2 = 3.0 x 1^2 = 3.0 kg-m/s
3.0 x 2 = 6.0
6.0 + 3.1 = 9.1 kg-m^2
Angular momentum = Inertia x omega
Inertia = 9.1
omega = 0.75 rad/s
9.1 x 0.75 = 6.825 kg-m^2/s
angular momentum after
Inertia of student = 3.0 kg-m^2
Inertia of weights = mr^2
3.0 x 0.32^2 = 0.3072 kg-m^2
0.3072 x 2 = 0.6144
3.0 + 0.6144 = 3.6144
6.825 kg-m^2/s = 3.6144 x omega
6.825/3.6144 = omega = 1.888 rad/s (answer)
(B)
Find the kinetic energy of the rotating system before and after he pulls the weights inward.
in J (before)
in J (after)
Rotational KE = 1/2I^2
Before = 0.5 x 9.1 x 0.75 ^2 = 2.559 J
After = 0.5 x 3.6144 x 1.888^2 = 6.441 J
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