A dancer is spinning at 72 rpm about an axis through her center with her arms ou

Question

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 56.5 kg, 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.

Calculate moment of inertia about dancer spin axis and rotational kinetic energy. Use the figures in the table 9.2 in the textbook to model reasonable approximations for the pertinent parts of your body.

Explanation / Answer

I = Ihead + Ibody + Iarms = mr^2 / 5 + mr^2/2 + 2m x r^2 / 3   

= 0.07 x 59 x 0.08^2 /5 + 0.80 x 59 x 0.12^2 /2 + 0.13 x 59 x 0.6^2 / 3

= 1.27 kg.m^2

B. R.K.E = Iw^2 /2

w = 72 x 2 xpi rad/ 60 sec = 7.54 rad/s

Rot . K.E. = 1.27 x 7.54^2 /2 =36.10 J

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