A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of i

Question

A 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 540 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth.

(a) In what direction does the turntable rotate?

counterclockwise or clockwise

With what angular speed does the turntable rotate?
? rad/s

(b) How much work does the woman do to set herself and the turntable into motion?
? J

Explanation / Answer

net angular momentum is conserved as there is no net external torque.
therefore. 0 = angular momenum of woman + angular momentum of wheel.

0 = 55x2x1.5 + 540x

= -0.3056 rad/sec ,-ve sign shows that the direction is opposite to woman, ie counterclockwise.

work done by woman = total kinetic energy of the wheel and woman

=1/2 x 55 x 1.52 + 1/2 I2 = 1/2x55x1.52 + 1/2x540x0.30562= 87.08J

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