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Suppose a 65-kg person stands at the edge of a 5.0-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1850 kg⋅m2. The turntable is at rest initially, but when the person begins running at a speed of 4.0 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction

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Calculate the angular velocity of the turntable.

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Mass of the person is 65 kg.

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Diameter of the merry-go-round is 5 m.

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Radius of the merry-go-round is 2.5 m.

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Moment of inertia of turntable is 1850 kg⋅m².

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Person is running at a speed of 4 m/sec.

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Angular momentum \"\", where \"\" is the moment of inertia and \"\" is the angular velocity.

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Moment of inertia is \"\".

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\"\"

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Angular velocity is \"\".

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\"\"

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Law of conservative of angular momentum:

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Angular momentum before the person starts running is equal to the angular momentum after the person starts running.

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\"\"

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\"\" is the moment of inertia of the person, \"\" is the angular velocity of the person.

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\"\" is the moment of inertia of the turntable,\"\" is the angular velocity of the turntable,

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\"\" is the total angular velocity.

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Initially turntable is at rest, hence \"\".

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Initially person runs with a speed \"\".

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Substitute the corresponding values in the law of conservative of angular momentum.

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\"\"

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Angular velocity of the turntable is 0.288 rad/sec.