Calculate Period of Leg of 1.75m Tall Man (68 kg)

[hot2moli]

The period of the leg can be approximated by treating the leg as a physical pendulum, with a period of , where I is the moment of inertia, m is the mass, and h is the distance from the pivot point to the center of mass. The leg can be considered to be a right cylinder of constant density. For a man, the leg constitutes 16 \% of his total mass and 48 \% of his total height.
Find the period of the leg of a man who is 1.75 m in height with a mass of 68 kg. The moment of inertia of a cylinder rotating about a perpendicular axis at one end is ml^2/3

________sec



Leg=10.88kg AND 0.84m

For the moment of inertia, what is the value for m and l?? is that the mass and length of the entire body?

 

[dynamicsolo]

... The leg can be considered to be a right cylinder of constant density. For a man, the leg constitutes 16 \% of his total mass and 48 \% of his total height.

... The moment of inertia of a cylinder rotating about a perpendicular axis at one end is ml^2/3

...

Leg=10.88kg AND 0.84m

For the moment of inertia, what is the value for m and l?? is that the mass and length of the entire body?

The values of m and l that you need are for the leg only, which you are asked to treat as a cylinder swinging about one end; the numbers are the ones you've already calculated.

 

[Moetasim]

The value for m and l in this scenario would refer to the mass and length of the leg specifically, as we are calculating the period of the leg. The mass of the leg can be calculated as 16% of the man's total mass, which is 68 kg, so the mass of the leg would be 0.16(68 kg) = 10.88 kg. The length of the leg can be calculated as 48% of the man's total height, which is 1.75 m, so the length of the leg would be 0.48(1.75 m) = 0.84 m. Plugging these values into the equation for the moment of inertia, we get I = (10.88 kg)(0.84 m)^2/3 = 6.12 kgm^2. Using this value for I and the given values for m and h in the equation for the period, we can calculate the period of the leg as T = 2π √(6.12 kgm^2/(10.88 kg)(9.8 m/s^2)(0.84 m)) = 0.89 seconds. So, the period of the leg of a man who is 1.75 m in height with a mass of 68 kg is approximately 0.89 seconds.