Torque required to rotate a circular sector inside a drum

AI Thread Summary
To calculate the torque required to rotate a solid circular sector within a 16’ x 72’ drum by 90 degrees, the moment of inertia of the sector must be determined first. The torque can be calculated using the formula Torque = Moment of Inertia x Angular Acceleration, where angular acceleration is derived from the angular velocity and time. The discussion highlights the need to consider both the moment of inertia of the drum and the circular sector, potentially applying the parallel axis theorem for accurate results. There is also a question regarding whether torque can be simplified to Torque = Force x Radius, with force being the mass times gravitational acceleration. Understanding angular acceleration and its calculation is essential for determining the required torque effectively.
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What I have ?
  • Have a 16’ x 72’ rotating drum
  • There is a solid circular sector inside the drum

What I need ?
Want to Calculate the torque required to move that solid circular sector from the intial position to the position shown in attached picture (90 Degrees rotation)


Data :
  • RPM = 10
  • time = 15 seconds


What I have caluted ?
  • Calculated the torque required to rotate the drum using Torque = Moment of Inertia X Alpha where Alpha = angular acceleration

How do I proceed ?
  1. Do I have to calculate the moment of inertia of that solid circular sector and then use the same formula?
  2. But here its not a complete rotation. Its just 90 degrees. So how to arrive at torque to move a mass about an axis only to a certain degree?
  3. Or, Should it be just Torque = Force * Radius ? where force shall be its mass * acceleration due to gravity and radius shall be distance from the drum's rotation axis to the circular sector's center of gravity ?
  4. Does Perpendicular axes theorem or Parallel Axes theorem come into the picture ?
 

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You will need to get the total moment of inertia of the drum + circular section. For that you may need the parallel axis theorem.

As for the rotation of the 90 degrees. What is the definition of angular acceleration?
 
rock.freak667 said:
You will need to get the total moment of inertia of the drum + circular section. For that you may need the parallel axis theorem.

As for the rotation of the 90 degrees. What is the definition of angular acceleration?

I am afraid , I didn't understand. My approach was to find the Inertia of both separately and then arrive at their individual torques. Did you mean the same ? Do we need a parallel axis theorem in that ? If yes, could you explain a little more elaborately ?

Angle was taken to be ∏/2.
Therefore, Angular Velocity = (∏/2)*rpm/60 = (∏/2)*10/60=.26 s^(-1)
and Angular acceleration = .26/time = .26/15 =0.0174 s^(-2)

Thanks for your help !
 

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