A runner of mass 56.0kg runs around the edge of a horizontal turntable mounted o

Question

A runner of mass 56.0kg runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 3.10m/s . The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.210rad/s relative to the earth. The radius of the turntable is 3.10m , and its moment of inertia about the axis of rotation is 81.0kg?m2

Question: Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.)

Explanation / Answer

mass of runner = m1 = 56 kg

radius of table == r = 3.1 m

velocity of runner = v1 = 3.1 m/s

Moment of inertia of table = I = 81 kg m^2

angular velocity of table = w1 = - 0.21 rad/s

Conservation of angular momentum

m 1 v1 r - I w1 = ( I + m1 r^2 ) w2

w2 = ( m 1 v1 r - I w1 ) / ( I + m1 r^2 )

w2 = ( 56 * 3.1 * 3.1 - 81 * 0.21 ) / ( 81 + 56*3.1*3.1 )

w2 = 0.842 rad/s

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final angular velocity of the system = 0.842 rad/s

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