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

`T = 1.108\,s`

Step-by-step explanation:

The period of a physical pendulum is:

`T = \sqrt{(I_(O))/(m\cdot g \cdot L) }`

`T=2\cdot \pi \sqrt{((1)/(3)\cdot m \cdot L^(2) )/(m\cdot g\cdot L) }`

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

`T = 1.108\,s`