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omky a search Q&A;! Chegg.com × ( Chapter 9)-Google Chrome 0 https://session masteringphysics.com/myct/fitemView?assignmentProblemID 44380253 PHY 231-004N (HYBRID) Spring2015 ( Tuesday) Signed in as ABDULLAH ALGANTANMHele Ceas ChapteProblem 9.92 e previous 9of9 return to Problem 9.92 Part A Human Rotational Energy. A dancer is spinning at 72 rpm about an axis through her center with her From biomedical measurements, the typica distribution of mass in a human body is as follows Calculate moment of inertia about dancer spin axois Use the figures in the folowing table to approximations for the pertinent parts of your body Express include the appropriato units model reasonable Head 70% Figure 1 1 2.3 kg·m12 Submit Incorrect, Try Again; 4 attempts remaining Part B Calcuate your otatonaietic energy

Explanation / Answer

The moment of inertia will be the sum of 3 elements: the head (a sphere), the trunk and legs (a cylinder) and the arms (two rods) placed at the border of the trunk, the mass of each element will be:

Head: 7% fo 61 Kg mh = 4.27 Kg

Trunk and legs 80%, mt = 48.8 Kg

Arms 13%, ma = 7.93 Kg

Now, let's calculate the moment of inertia for each part:

For the head Ih = (2/5) mh (Rh)2 = 0.01 Kg m2

For the trunk It = (1/2) mt (Rt)2 = 0.35 Kg m2

Arms: Ia = ma (Rt)2 + (1/3) ma (La)2 = 1.4 Kg m2

Where R are the radios of head and trunk, and La is the arm length

The first term for the moment of inertia of the arms comes from the parallel axis theorem

Thus I = 1.4 Kg m2 (part a)

Part b)

72 rpm = 1.2 turns per second

w = 1.2 s-1

Kw = (1/2) I w2 = 1.008 joule 1.0 joule

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