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 60.5 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. (Figure 1)

1.) Calculate moment of inertia about dancer spin axis. Use the figures in the table 9.2 in the textbook to model reasonable approximations for the pertinent parts of your body. Express your answer to two significant figures and include the appropriate units.

2.) Calculate your rotational kinetic energy. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

here,

mass of the dancer ,m = 60.5 kg

mass of head , mh = 7 % of 60.5

mh = 4.235 kg

mass of Arms , ma = 13 % of 60.5

ma = 7.865 kg

mass of trunk and legs , mt = 80% of 60.5

mt = 48.4 kg

a)

let the arms have shape of uniform rod and head na dtrunk are in shape of cyclinder

the moment of inertia , I = 0.5 * mt * 0.12^2 + 0.5 * mh * 0.08^2 + ma * 0.6^2 /3

I = 0.5 * 48.4 * 0.12^2 + 0.5 * 4.235 * 0.08^2 + 7.865 * 0.6^2 /3

I = 1.31 kg.m^2

the moment of inertia of the dancer is 1.31 kg.m^2

b)

w = 72 rpm

w = 7.536 rad/s

the rotational kinetic energy , KE = 0.5 * I * w^2

KE = 0.5 * 1.31 * 7.536^2

KE = 37.2 J

the required kinetic energy is 37.2 J

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