A playground turntable is in the form of a solid wheel. It has mass of 600 kg, a

Question

A playground turntable is in the form of a solid wheel. It has mass of 600 kg, a radius of 3 meters and is initially at rest. A child begins to push tangentially on the edge of the table with a force of 200 N over an angle of rotation of 1 radian. Determine the moment of inertia. Determine the final energy of the rotating table, the final angular velocity and the final angular momentum table. How long was the child pushing? In problem 4 assume the same turntable is originally rotating at a r/s. Assume a child sitting in the exact center of the table and contributing nothing to the inertia of the table then slides to the edge of the table. If the child's mass is 50 kg what will be the new rotation rate of the table when the child reaches the edge of the table?

Explanation / Answer

4: moment of inertia = M R^2 /2

= 600 x 3^2 / 2

= 2700 kg m^2

torque = I alpha

200 x 3 = 2700 alpha

alpha = 0.22 rad/s^2

wf^2 - wi^2 = 2 alpha theta

w^2 - 0^2 = 2 (0.22)(1)

w = 0.67 rad/s ...........Final angular velocity

final angular momentum = I w = 2700 x 0.67

= 1800 kg m^2 /s

final energy = I w^2 / 2

= 2700 x 0.67^2 / 2
= 600 J

wf = wi + alpha t

0.67 = 0 + 0.22 t

t = 3 sec

5: Applying angular momentum conservation,

Ii wi = If wf

(2700) (4) = (2700 + (50 x 3^2)) wf

wf = 3.43 rad/s

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