A student sits on the rotatable stool holding a bicycle wheel that is spinning i
ID: 2259917 • Letter: A
Question
A student sits on the rotatable stool holding a bicycle wheel that is spinning in the horizontal plane. Let's assume the wheel has a mass of 5kg with a radius of 0.3m, and all the mass is concentrated at the edge. She flips the rotation axis of the wheel 180o, and finds that she herself starts to rotate. The student and the chair have a moment of inertia of I=70 kg m^2.
Initially the student holds the wheel so that it spins with angular velocity w= 60 rad/sec about a vertical axis. ( it is held sideways rotating in a horizontal plane). The student quickly flips the wheel so that the axis remains vertical, but the wheel now rotates in the opposite direction. The student will start to rotate on the stool. How fast will she be rotating when the wheel is flipped.
Explanation / Answer
moment of inertia of wheel = m*r^2 = 5*0.3^2 = 0.45 kg-m^2 from conservation of angular momentum; intial angular momentum = final angualr momentum => I*w = - I'*w' => 0.45*60 = -(0.45 +70)*w => w = -0.383 rad/s -ve sign shows that the wheel is rotating in the opposite direction as before.
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