A person with mass mp = 72 kg stands on a spinning platform disk with a radius o

Question

A person with mass mp = 72 kg stands on a spinning platform disk with a radius of R = 1.71 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 0.57 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?

Explanation / Answer

I_disk = ½MR² = ½ * 194kg * (1.71m)² = 283.64 kg·m²

1) I = I_disk + mR² = 283.64 kg·m² + 72kg * (1.71m)² = 494.17 kg·m²

2) I' = 283.64 kg·m² + 72kg * (1.71m/3)² = 307.03 kg·m²

3) I* = I'*'
494.17kg·m² * 1.9rad/s = 307.03 kg·m² * '
' = 3.06 rad/s

4) initial KE = ½I² = ½ * 494.17kg·m² * (1.9rad/s)² = 891.98 J
final KE' = ½ * 307.03kg·m² * (3.06rad/s)² = 1437.45 J
KE = 545.47 J

5) a = ²r = (3.06 rad/s)² * 1.71m/3 = 5.34 m/s²

6) = 1.9 rad/s
(angular momentum is conserved)

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