A professor doing a lecture demonstration stands at the center of a frictionless

Question

A professor doing a lecture demonstration stands at the center of a frictionless turntable, holding 5.00?kg masses in each hand with arms extended so that each mass is 0.850m from his centerline. A (carefully selected!) student spins the professor up to a rotational frequency of 27.3rpm. If he then pulls his arms in by his sides so that each mass is 0.370m from his centerline, what is his new angular speed? Assume that his rotational inertia without the masses is 4.11kg?m2, and neglect the effect on the rotational inertia of the position of his arms, since their mass is small compared to the mass of the body.

Explanation / Answer

I1 w1 = I2 w2

(I0 + 2 m (r1)^2) w1 = (I0 + 2 m (r2)^2) w2

==> (I0 + 2 m (r1)^2) (2 pi f1) = (I0 + 2 m (r2)^2) (2 pi f2)

(4.11 + 2*5*(0.850^2)) * (27.3/60) = (4.11 + 2*5*(0.370^2)) * f2

==> f2 = 0.941 Hz = 0.941 s^-1

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