# Calculate the new angular velocity of the disc

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? wont r=0?

## Answers and Replies

rl.bhat
Homework Helper
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.

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?

LowlyPion
Homework Helper
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)

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?

LowlyPion
Homework Helper
Right you are. Transcription error:

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