A 62.0-kg woman stands at the western rim of a horizontal turntable having a mom

Question

A 62.0-kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 505 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 counterdockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. Consider the woman-turntable system as motion begins. (a) Is the mechanical eneroy of the system constant? Yes No (b) Is the momentum of the system constant? (e) Is the angular momentum of the system constant? Yes o No (d) In what direction and with what angular speed does the turntable rotate? magnitude direction clockwise rad/s (e) How much chemical energy does the woman's body convert into mechanical energy of the woman-turntable system as the woman sets herself and the turntable into motion?

Explanation / Answer

(L1 + L2)(i) = (L1 + L2)(f)

0 = I11 + I22

1 = - I22 / I1

= v / r

So replacing 2 with v / r and I2 with mr2 we have:

1 = -mr2/r / I = -mrv / I1 = -(62 kg)(2.0 m)(-1.5m/s) / 500kgm2 = 0.372 rad/s (counter-clockwise)

The work she does to get the turntable to this speed is found from the work-energy theorem, where the net work is equal to the change in kinetic energy:

W = KE

= KE(f) - KE(i) = [0.5I112 + 0.5mv22] - 0

= [0.5 (500kgm2)(0.372 rad/s)2 + 0.5(62kg)(-1.5m/s)2] = 104.35 J

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