Final answer:
The moment of inertia for a solid sphere about an axis through its center is 2/5 MR². For a solid sphere with a radius of 0.2 m and mass of 1.0 kg, the moment of inertia is 0.016 kg • m².
Step-by-step explanation:
Moment of Inertia for a Solid Sphere
The moment of inertia (I) for a solid sphere about an axis through its center of mass is given by the formula I = 2/5 MR², where 'M' is the mass of the sphere and 'R' is the radius of the sphere. In a scenario where we have a solid sphere with a radius of 20.0 cm (or 0.2 m) and a mass of 1.0 kg, plugging these values into the formula gives us:
I = (2/5)(1.0 kg)(0.2 m)²
I = (2/5)(1.0 kg)(0.04 m²)
I = (2/5)(0.04 kg • m²)
I = 0.016 kg • m²
Therefore, the moment of inertia of this solid sphere is 0.016 kg • m².
This concept is crucial in rotational dynamics and is essential for understanding how objects rotate about different axes and the distribution of their mass.