Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through he

Question

Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in the following figure. From biomedical measurements, the typical distribution of mass in a human body is as follows:

Head: 7.0%

Arms: 13%(for both)

Trunk and legs: 80.0%

Suppose the mass of the dancer is 55.0 kg, the diameter of her head is 16cm, the width of her body is 24cm, and the length of her arms is 60cm

Calculate moment of inertia about dancer spin axis. Use the figures in the following table to model reasonable approximations for the pertinent parts of your body.

Calculate your rotational kinetic energy.

Explanation / Answer

mass of the head is 0.07*55 = 3.85 Kg

mass of arms = 0.13*55 = 7.15 Kg

mass of trunk and legs = 0.8*55 = 44 kg

moment of inetria of the dancer is I = (1/5)*m*r^2 + (1/2)*m*r^2 + (2/3)*m*r^2)

I = ((1/5)*3.85*0.08^2)+((1/2)*44*0.12^2))+((2/3)*7.15*0.6^2) =

I = 2.03 Kg-m^2

rotational kinetic energy

KE = 0.5*I*w^2

w = 72 rpm = 72*(2*3.142/60) = 7.54 rad/s

then

KE = 0.5*I*w^2 = 0.5*2.03*7.54^2 = 57.7 J

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