Physics Homework Help?

Question

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

Calculate the angular velocity of the turntable.

Answer 1

Mass of the person is 65 kg.

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

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

Moment of inertia of turntable is 1850 kg⋅m².

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

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

Moment of inertia is .

Angular velocity is .

Law of conservative of angular momentum:

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

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

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

is the total angular velocity.

Initially turntable is at rest, hence .

Initially person runs with a speed .

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

Angular velocity of the turntable is 0.288 rad/sec.