Question

Find the period of the leg of a man who is 1.83 m in height with a mass of 67 kg. The moment of inertia of a cylinder rotating about a perpendicular axis at one end is ml2/3.

Answer 1

Answer:

$T = 1.108\,s$

Explanation:

The period of a physical pendulum is:

$T = \sqrt{\frac{I_{O}}{m\cdot g \cdot L} }$

$T=2\cdot \pi \sqrt{\frac{\frac{1}{3}\cdot m \cdot L^{2} }{m\cdot g\cdot L} }$

$T=2\cdot \pi \sqrt{\frac{L }{3\cdot g} }$

The length of the leg is approximately the height of the person:

$L = 0.915\,m$

The period is:

$T = 2\cdot \pi \sqrt{\frac{0.915\,m}{3\cdot (9.807\,\frac{m}{s^{2}} )} }$

$T = 1.108\,s$