A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and

Question

A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 9.00 kg ,while the balls each have mass 0.300 kg and can be treated as point masses.

Part A

Find the moment of inertia of this combination about an axis perpendicular to the bar through its center.

Part B

Find the moment of inertia of this combination about an axis perpendicular to the bar through one of the balls.

Part C

Find the moment of inertia of this combination about an axis parallel to the bar through both balls.

PART D

Find the moment of inertia of this combination about an axis parallel to the bar and 0.500 m from it.

Explanation / Answer

moment of inertia of this combination about an axis perpendicular to the bar through its center

I = ML²/12 + 2 * mr² = (1/12)(9kg)(2m)² + 2 * 0.3kg * (1m)² = 3.6 kg·m²

By the parallel axis theorem,

I = 3.6kg·m² + (9 + 2*0.3)kg*(0.5m)² = 6 kg·m²

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