Question

A dancer is spinning at 72 about an axis through her center with her arms outstretched, as shown in the following figure. From biomedical measurements, the typicaldistribution 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 65.0kg , the diameter of her head is 16cm , the width of her body is 24cm , and the length of her arms is 60cm .

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 yourbody.

Answer 1

Moment of inertia of the headI₁ = 7% of moment of inertia of asphere 0.07 (2/5)mR^2= 0.07 (65)(2/5)(0.08)^2= 0.011648 kg m^2moment of inertia of bodyI₂ = 80% of moment of inertia of cylinder= (0.8) (1/2)mR^2 = 0.8(1/2)(65)(0.12)^2= 0.3744kg m^2moment of inertia of both armsI₃ = 0.13(2) (1/3)mL^2= 0.13(2/3)(65)(0.6m)^2= 2.028kg m^2total moment of inertia isI = I1 = I2 +I3= 2.414 kg m^2