Question

Suppose we want to calculate the moment of inertia of a 56.5 kg skater, relative to a vertical axis through their center of mass.

Required:
a. First calculate the moment of inertia (in kg-m²) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.11 m.

Answer 1

The moment of inertia of a 56.5 kg skater, approximated as a solid cylinder with a radius of 0.11 m, is 0.34 kg·m².

Step-by-step explanation:

To calculate the moment of inertia (I) of a 56.5 kg skater, who is approximated as a cylinder with a radius (r) of 0.11 m, we use the formula for the moment of inertia of a solid cylinder which is:

I = (1/2)MR²,

where M is the mass of the cylinder and R is the radius. Plugging in the values we get:

I = 0.5 × 56.5 kg × (0.11 m)²

I = 0.5 × 56.5 kg × 0.0121 m²

I = 0.341575 kg·m² or approximately I = 0.34 kg·m² after rounding to two decimal places.