Question

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 kgkg dumbbell in each hand (Figure 1). He is set rotating about a vertical axis, making one revolution in 2.0 ss. His moment of inertia (without the dumbbells) is 3.4 kg⋅m2kg⋅m2 when his arms are outstretched, and drops to 1.8 kg⋅m2kg⋅m2 when his arms are pulled in close to his chest. The dumbbells are 1.0 mm from the axis initially and 0.20 mm 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.

Answer #1

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...

A person stands at the center of a turntable, holding his arms
extended horizontally with a 1.5 kg dumbbell in each hand. He is
set rotation about a vertical axis, making one revolution in 2
seconds. Find the new angular velocity if he pulls the dumbbells in
to his middle. His moment of inertia (without dumbbells) is 3 kgm2
when his arms are out stretched, dropping to 2.2 kgm2 when his
hands are at his middle. The dumbbells are 1...

A student sits on a freely rotating stool holding two dumbbells,
each of mass 2.91 kg (see figure below). When his arms are extended
horizontally (Figure a), the dumbbells are 1.03 m from the axis of
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rad/s. The moment of inertia of the student plus stool is 2.61 kg ·
m2 and is assumed to be constant. The student pulls the
dumbbells inward horizontally to a position 0.297 m...

A physics teacher does a classroom demonstration on a rotating
table illustrating angular momentum. His body has a moment of
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and with his arms outstretched, he begins spinning at 27 rpm. The
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The outstretched hands and arms of a figure skater preparing for
a spin can be considered a slender rod pivoting about an axis
through its center. (See the figure below (Figure 1).) When the
skater's hands and arms are brought in and wrapped around his body
to execute the spin, the hands and arms can be considered a
thin-walled hollow cylinder. His hands and arms have a combined
mass of 7.5 kgkg . When outstretched, they span 1.8 mm ;...

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