Question

Human Rotational Energy. 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 that 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. Use the figures in the following table to model reasonable approximations for the pertinent parts of your body Express your answer to two significant figures and include the appropriate units. Calculate your rotational kinetic energy. Express your answer to two significant figures and include the appropriate units.

Answer 1

a) moment of inertia of head = 0.5mr^2 = 0.5*0.07*56.5*0.08^2 = 0.012656 kg m^2
moment of inertia of trunk and legs = 0.5mr^2 = 0.5*0.8*56.5*0.24^2 = 1.30176 kg m^2
moment of inertia of arms = 0.5mr^2 = 0.5*0.13*56.5*0.6^2 = 1.3221 kg m^2
Total I = 2.636516 kg m^2

b) k = 0.5Iw^2 = 0.5*2.63*72*2pi/60 = 9.934 J