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Sanjay and Ting, each with a mass of 25 kg, are riding opposite each other on the edge of a 150 kg,

3.0-m-diameter playground merry-go-round that's rotating at 23 rpm. Each walks straight inward and
stops 35 cm from the center.
What is the new angular velocity, in rpm?

User Tovah
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2 Answers

5 votes

Final answer:

To find the new angular velocity, we use the principle of conservation of angular momentum. The new moment of inertia can be calculated using the equation If = Ii + ms * rs2. Substituting the values, we find that the new angular velocity is approximately 30.64 rpm.

Step-by-step explanation:

To calculate the new angular velocity of the merry-go-round, we can use the principle of conservation of angular momentum. Initially, the angular momentum of the system is given by: Li = Ii * ωi, where Li is the initial angular momentum, Ii is the initial moment of inertia, and ωi is the initial angular velocity.

When the students move towards the center, their moment of inertia changes, but the total angular momentum of the system remains constant. The new moment of inertia can be calculated using the equation: If = Ii + ms * rs2, where If is the final moment of inertia, ms is the mass of the student, and rs is the distance of the student from the axis of rotation.

Substituting the values into the equation and solving for the new angular velocity, we get: ωf = Li / If.

After substituting the given values, the new angular velocity is approximately 30.64 rpm. Therefore, the new angular velocity of the merry-go-round is 30.64 rpm.

User Megloff
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4 votes

Final answer:

The problem involves the conservation of angular momentum to determine the new angular velocity when two children on a merry-go-round move closer to the center. Initial and final angular momenta are equated, and the change in moment of inertia is calculated to solve for the new rotational speed in rpm.

Step-by-step explanation:

The student's question relates to the concept of conservation of angular momentum in physics. When Sanjay and Ting, each with a mass of 25 kg, move inward on a merry-go-round, they change the distribution of mass and thus the moment of inertia of the system. Initially, the merry-go-round is rotating at 23 revolutions per minute (rpm).

Since angular momentum (L) is conserved,

we can set the initial angular momentum equal to the final angular momentum (Li = Lf).

The moment of inertia (I) of a point mass at a distance (r) from the axis of rotation is I = mr2,

and the angular momentum L = Iω,

where ω is the angular velocity. The initial moment of inertia for each child is (25 kg)(1.5 m)2 since the diameter is 3.0 m.

When both children move to 35 cm (0.35 m) from the center, the new moment of inertia for each child is (25 kg)(0.35 m)2.

The total change in moment of inertia must account for both children and the merry-go-round itself, which does not change.

To find the new angular velocity, set the initial angular momentum (which includes the combined moment of inertia of the merry-go-round and both children at the edge) equal to the final angular momentum (which includes the new combined moment of inertia with the children 35 cm from the center).

Solve for the new angular velocity. The result will be in radians per second, which can be converted back to rpm for the final answer.

User Minni
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