A disk-shaped merry-go-round of radius 2.83 m and mass 185 kg rotates freely with an angular speed of 0.701 rev/s . A 63.4 kg person running

Question

A disk-shaped merry-go-round of radius 2.83 m and mass 185 kg rotates freely with an angular speed of 0.701 rev/s . A 63.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round’s rim. Part A What is the final angular speed of the merry-go-round

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5 months 2021-08-23T20:28:39+00:00 1 Answers 10 views 0

The final angular speed of the merry-go-round is .

Explanation:

Given the absence of external forces, the final angular speed of the merry-go-round can be determined with the resource of the Principle of Angular Momentum Conservation, which is described in this case as:

Where:

– Moment of inertia of the merry-go-round with respect to its axis of rotation, measured in .

– Moment of inertia of the person with respect to the axis of rotation of the merry-go-round, measured in .

– Initial angular speed of the merry-go-round with respect to its axis of rotation, measured in radians per second.

– Initial angular speed of the merry-go-round with respect to the axis of rotation of the merry-go-round, measured in radians per second.

– Final angular speed of the merry-go-round-person system, measured in radians per second.

The final angular speed is cleared:

Merry-go-round is modelled as uniform disk-like rigid body, whereas the person can be modelled as a particle. The expressions for their moments of inertia are, respectively:

Merry-go-round

Where:

– The mass of the merry-go-round, measured in kilograms.

– Radius of the merry-go-round, measured in meters.

Person

Where:

– The mass of the person, measured in kilograms.

– Distance of the person with respect to the axis of rotation of the merry-go-round, measured in meters.

If , , , the moments of inertia are, respectively:

The angular speed experimented by the person with respect to the axis of rotation of the merry-go-round is:

Given that , , and , the final angular speed of the merry-go-round is:

The final angular speed of the merry-go-round is .