A physics student is standing on an initially motionless, frictionless turntable

Question

A physics student is standing on an initially motionless, frictionless turntable with rotational inertia 0.31 kgm2. She's holding a wheel with rotational inertia 0.22 kgm2spinning at 130 rpm about a vertical axis, as in the figure. (Figure 1) When she turns the wheel upside down, student and turntable begin rotating at 70 rpm.

https://session.masteringphysics.com/problemAsset/2096200/1/11.40.jpg

1. Find the student's mass, considering her to be a 30-cm-diameter cylinder.

(in kg)

2.

Neglecting the distance between the axes of the turntable and wheel, determine the work she did in turning the wheel upside down.

( in J)

Explanation / Answer

a)

Since the turn table is frictionless, there are no external torques about its axis, and the z component of
angular momentum is conserved. Initially this is all spin of the wheel,

L0 = (0.22 kg m )(137 rpm).

When the wheel is inverted, the student and turrable acquire anugular momentum, L z such that

Lz = I tot (72 rpm) = 2(0.22 kg m 2 )(137 rpm)

I tot = 0.837 kg m 2

the student (a cylinder0, (1/2)M(0.5 m)2, and CM of thewheel, can be neglected if the axes of the wheel and turntable coincide, and the spin axis isfrictionless).

Then (1/2)M(0.15 m)2=(0.837-0.31) kg m2

M = 46.84kg.

(b)

The work done by the student’s muscle equals the change in kinetic energy,

Wnc = K = (1 / 2) I tot 2

Wnc = (1 / 2)(0.837 kg m )(72 / 30 s)2

= 23.79 J.

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