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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Solved: BIO Human Rotational Energy. A dancer is spinning

Chapter 9, Problem 9.92

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QUESTION:

Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in Fig. P9.92. 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 you are this dancer. Using this information plus length measurements on your own body, calculate (a) your moment of inertia about your spin axis and (b) your rotational kinetic energy. Use the figures in Table 9.2 to model reasonable approximations for the pertinent parts of your body.

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QUESTION:

Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in Fig. P9.92. 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 you are this dancer. Using this information plus length measurements on your own body, calculate (a) your moment of inertia about your spin axis and (b) your rotational kinetic energy. Use the figures in Table 9.2 to model reasonable approximations for the pertinent parts of your body.

ANSWER:

Step 1 of 6

a) Suppose, the height of the dancer is 180 cm and mass of the dancer is 65 kg

Then, the mass of the head,  = (7/100) 65 kg = 4.55 kg

Then, the mass of the trunk and legs,  = (80/100) 65 kg = 52 kg

Then , the mass of the arms,  = (13/100) 65 kg = 8.45 kg

Consider, the diameter of head as, D = 15 cm

Consider the height of the person up to shoulders as, H = 165 cm

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