In this example we see how a system can have constant angular momentum without having a constant angular velocity! A physics professor stands at the center of a turntable, holding his arms extended horizontally, with a 5.0 kg dumbbell in each hand (Figure 1). He is set rotating about a vertical axis, making one revolution in 2.0 s. His moment of inertia (without the dumbbells) is 3.4 kg⋅m2 when his arms are outstretched, and drops to 1.8 kg⋅m2 when his arms are pulled in close to his chest. The dumbbells are 1.0 m from the axis initially and 0.20 m from it at the end. Find the professor's new angular velocity if he pulls the dumbbells close to his chest, and compare the final total kinetic energy with the initial value.
Suppose the professor drops the dumbbells and then pulls his arms in close to his chest. What is his final angular velocity?
Express your answer in revolutions per second to two significant figures.
Solution in the uploaded images
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