A thin, uniform circular plate of mass and radius spins at about its central axis.…

PHYSICS · Subjective · A Level · Physics · Engineering physics · Engineering physics

Problem

A thin, uniform circular plate of mass 2.5 kg2.5\,\text{kg} and radius 0.40 m0.40\,\text{m} spins at 8.0 rad/s8.0\,\text{rad/s} about its central axis. Three small objects are on the plate: • Object 1: mass 0.60 kg0.60\,\text{kg} at the rim (0.40 m0.40\,\text{m} from the center). • Object 2: mass 0.60 kg0.60\,\text{kg} located 0.20 m0.20\,\text{m} from the center. • Object 3: mass 0.40 kg0.40\,\text{kg} moving in a circle of radius 0.30 m0.30\,\text{m} around the center; its speed relative to the ground is 4.4 m/s4.4\,\text{m/s} because it moves 2.0 m/s2.0\,\text{m/s} faster than the local surface of the plate in the same tangential direction. Determine the magnitude of the total angular momentum of the entire system (plate plus three objects) about the plate’s center at this instant.

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