A person with mass m p = 77 kg stands on a spinning platform disk with a radius

Question

A person with mass mp = 77 kg stands on a spinning platform disk with a radius of R = 2.16 m and mass md = 194 kg. The disk is initially spinning at ? = 1.9 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.72 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?
kg-m2

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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?
kg-m2

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3)

What is the final angular velocity of the disk?
rad/s

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4)

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

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5)

What is the centripetal acceleration of the person when she is at R/3?
m/s2

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6)

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

A person with mass mp = 77 kg stands on a spinning platform disk with a radius of R = 2.16 m and mass md = 194 kg. The disk is initially spinning at ? = 1.9 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.72 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? kg-m2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 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? kg-m2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the final angular velocity of the disk? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.) J You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the centripetal acceleration of the person when she is at R/3? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) If the person now walks back to the rim of the disk, what is the final angular speed of the disk? rad/s

Explanation / Answer

Original MI = 77 * 2.16^2 + 1/2 * 194 * 2.16^2 = 811.814 kgm^2

Final MI = 77 * 0.72^2 + 522.9 = 562.81 kgm^2

Original L =811.814 * 1.9 = final L = 562.81 w

w = 3.03 = 3.0 rad/s

Original KE = 1/2 * 811.814 * 1.9^2 = 1465.324 J

Final KE = 1/2 * 562.81 * 3.03^2 = 2583.551 J

Gain in KE = 1118 = 1200 J

w^2 r = centripetal acceleration = 3.03^2 . 0.72 = 6.61 m/s/s

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