The mass of the sphere is 0.151 kg. What is the rotational inertia of the wheel

Complete Question:

The mass of the sphere is 0.151 kg. What is the rotational inertia of the wheel? Recall that the radius of the sphere is about 0.312 m. Express your answer with three significant figures in Kg. m².

Answer:

I = 5.88*10⁻³ kg. m²

Explanation:

It can be showed that the rotational inertia (or moment of inertia) for a solid sphere of radius r and mass m, regarding any axis passing through the center of the sphere, can be expressed as follows:

I = (2/5) * m*r² (1)

where m = 0.151 kg, and r = 0.312 m. (Our givens).

Replacing in (1) we have:

I = (2/5) * 0.151 kg * (0.312m) ² = 5.88*10⁻³ kg. m²