A student sitting on a stool that can rotate freely. The student holds a bicycle
ID: 2077040 • Letter: A
Question
A student sitting on a stool that can rotate freely. The student holds a bicycle wheel rotating around the vertical axes. The moment of inertia of the student is I_student and the moment of inertia of the bicycle wheel is I_bicycle- The angular velocity of the bicycle wheel is omega_wheel and the angular velocity of the student sitting on the stool is omega_student = 10 rad/sec. The students turns the wheel at 90 degrees (the wheel is rotating after the turn in the perpendicular direction such that the angular velocities (omega_wheel and omega_student are perpendicular to each other. a) Assuming that the stool only can rotate around the vertical axes, find the angular velocity of the student after he turns the wheel at 90 degrees.Explanation / Answer
a] When the axis of the rotation of wheel is vertical, both the student and the wheel rotate in the same plane. Conservation of angular momentum tells that if the angular velocity of the student is 10 rad/s, then the wheel is turning with an angular velocity of - 10 rad/s in the opposite direction so that the net torque on the system is zero.
When the wheel is rotated by 90 degrees such that its axis of rotation is now horizontal, then there is no turning effect in the direction of rotation of the student and so the student will come to rest. Therefore its angular velocity will become 0 rad/s after turning the wheel.
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