Calculate the new angular velocity of the disc

AI Thread Summary
To calculate the new angular velocity of a disc when a mass moves from the edge to the center, the conservation of angular momentum principle is applied. The initial total angular momentum is determined by the sum of the moments of inertia of both the disc and the person, multiplied by the initial angular velocity. As the person walks to the center, the moment of inertia changes, leading to a new angular velocity. The correct formula incorporates the initial angular velocity to maintain angular momentum conservation. The final angular velocity can be expressed as ω_new = Total angular momentum / (1/2 * M_disk * r^2).
rawimpact
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1. Tim of a mass of 50 kg is standing on a large spinning disc of a mass of 80kg and a diameter of 5m. Tim standing at the edge of the disc which is rotating at 25 rad/s. He then walks to the center of the disc. Calculate the new angular velocity of the disc.
2. IW=I'W'
IdiskWdisk + ImitchWmitch = ItotalWdisk <-- Is this correct?
Idisk = 1/2mr^2
Imitch = mr^2
W' = 25rad/s

3. I was wondering how to do this problem? The inertia for a standing object = mr^2 and inertia for the disk = 1/2mr^2. How do i change the equation to show his location final? won't r=0?
 
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When the object is at the edge the total moment of inertia is the sum of the MI of disk and MI of Tim. When Tim moves to the center of the disk, the MI is due to the disk only.
 
rl.bhat said:
When the object is at the edge the total moment of inertia is the sum of the MI of disk and MI of Tim. When Tim moves to the center of the disk, the MI is due to the disk only.

IdiskWdisk + ImitchWmitch = IdiskW'

correct?
 
rawimpact said:
IdiskWdisk + ImitchWmitch = IdiskW'

correct?

For the most part.

ω is the same for both boy and disk initially.

1/2Mdisk*r2 + Mboy*r2 = Total angular momentum.

Total = Idisk * ω_new

ω_new = Total / (1/2*Mdisk*r2)
 
LowlyPion said:
For the most part.

ω is the same for both boy and disk initially.

1/2Mdisk*r2 + Mboy*r2 = Total angular momentum.

Total = Idisk * ω_new

ω_new = Total / (1/2*Mdisk*r2)


what happened to the ω_initial?
 
Right you are. Transcription error:

(1/2Mdisk*r2 + Mboy*r2) * ω_initial = Total angular momentum.
 
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