Question

Calculate the rotational inertia of each of the following uniform objects about the axes indicated: a) A thin 2.5 kg rod of length 0.75 m, about an axis perpendicular to it and passing through its center. b) A 3 kg thin walled hollow sphere 0.38 m in diameter, about an axis (i) through its center, and (ii) tangent to the edge of the sphere

Answer 1

a. I₁ = 0.1171875 kg * m²

b. I₂ = 0.288 kg * m²

Step-by-step explanation:

a. m₁ = 2.5 kg, L₁ = 0.75 m

The rotational inertia about an axis perpendicular to it and passing through its center

I₁ = ¹/₁₂ * M * L²

I₁ = ¹/₁₂ * 2.5 kg * (0.75m)²

I₁ = 0.1171875 kg * m²

b. m₂ = 3 kg , d₁ = 0.38 m

The rotational inertia tangent to the edge of the sphere

I₂ = ²/₃ * M * R²

I₂ = ²/₃ * 3 kg * (0.38m)²

I₂ = 0.288 kg * m²