Human Rotational Energy. A dancer is spinning at 72 rpmabout an axis through her

Question

Human Rotational Energy. A dancer is spinning at 72 rpmabout 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 58.5kg , the diameter of her head is 16 cm, the width of her body is 24 cm, and the length of her arms is 60 cm.

Part A

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.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

from the given data,

mass of head, m1 = 0.07*58.5 = 4.095 kg

Radius of head, R = d/2 = 16/2 = 8 cm = 0.08 m

mass of Arm, m2 = 0.13*58.5 = 7.605 kg

Length of arms, L = 60 cm = 0.6 m

mass of Trunk and legs, m3 = 0.8*58.5 = 46.8 kg

Width of the body, W = 24 cm = 0.24 m

Total moment of Inerta, I = I_head + I_arms + I_trunkandlegs

= (2/5)*m1*R^2 + m2*(2*L)^2/12 + m3*w^2/12

= (2/5)*4.095*0.08^2 + 7.605*(2*0.6)^2/12 + 46.8*0.24^2/12

= 1.148 kg.m^2 <<<<<---------Answer

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