A person with mass m p = 73 kg stands on a spinning platform disk with a radius

Question

A person with mass mp = 73 kg stands on a spinning platform disk with a radius of R = 2.04 m and mass md = 199 kg. The disk is initially spinning at = 1.5 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.68 m from the center).

1)

What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?

2)

What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk?

3)

What is the final angular velocity of the disk?

4)

What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.)

5)

What is the centripetal acceleration of the person when she is at R/3?

6)

If the person now walks back to the rim of the disk, what is the final angular speed of the disk?

Explanation / Answer

here,

mp = 73 kg,

R = 2.04 m

md = 199 kg

initial angular speed , w0 = 1.5 rad/s

1)

the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk , Ii = 0.5 *md*R^2 + mp * R^2

Ii = 0.5 * 199 * 2.04^2 + 73 * 2.04^2

Ii = 717.88 kg.m^2

the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk is 717.88 kg.m^2

2)

the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk

If = 0.5 *md*R^2 + mp * (R/3)^2

If = 0.5 * 199 * 2.04^2 + 73 * (2.04/3)^2

If = 447.83 kg.m^2

the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk is 447.83 kg.m^2

3)

let the final angular speed be w

using conservation of angular momentum

Ii * w0 = If * w

w = 2.4 rad/s

the final angular velocity of the disk is 2.4 rad/s

4)

the change in total kinetic energy

KE = KEf - KEi

KE = 0.5 * If*w^2 - 0.5 * Ii*w0^2

KE = 0.5 * 447.83 * 2.4^2 - 0.5 * 717.88*1.5^2

KE = 482.14 J

the change in total kinetic energy of the system is 482.14 J

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