Calculate the new angular velocity of the disc

In summary, Tim standing on a spinning disk of a mass of 80kg and a diameter of 5m, initially rotating at 25 rad/s, moves to the center of the disk. The new angular velocity of the disk can be calculated using the equation (1/2Mdisk*r2 + Mboy*r2) * ω_initial = Total angular momentum, where ω_initial is the initial angular velocity.
  • #1
rawimpact
14
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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)
 
  • #5
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?
 
  • #6
Right you are. Transcription error:

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

1. What is the formula for calculating the new angular velocity of a disc?

The formula for calculating the new angular velocity of a disc is: ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.

2. How do you determine the initial angular velocity of a disc?

The initial angular velocity of a disc can be determined by dividing the initial angular displacement by the initial time. This can also be calculated by using the formula ω0 = Δθ / Δt, where ω0 is the initial angular velocity, Δθ is the initial angular displacement, and Δt is the initial time.

3. Can the new angular velocity of a disc be negative?

Yes, the new angular velocity of a disc can be negative. This indicates that the disc is rotating in the opposite direction as its initial rotation.

4. How does the angular acceleration affect the new angular velocity of a disc?

The angular acceleration directly affects the new angular velocity of a disc. A higher angular acceleration will result in a larger change in the angular velocity, while a lower angular acceleration will result in a smaller change in the angular velocity.

5. Is it necessary to know the initial angular displacement to calculate the new angular velocity of a disc?

No, it is not necessary to know the initial angular displacement to calculate the new angular velocity of a disc. As long as the initial and final times, initial and final angular velocities, and angular acceleration are known, the new angular velocity can be calculated using the formula ω = ω0 + αt.

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