What Torque is Needed to Rotate a Solid Bored Ball?

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Discussion Overview

The discussion revolves around calculating the torque required to rotate a solid bored ball, focusing on the moment of inertia and its relationship to torque and angular acceleration. The context includes theoretical and mathematical reasoning related to the mechanics of rotating bodies.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant outlines the parameters for calculating torque, specifying a solid ball with a bore and its rotation about a specific axis.
  • Another participant suggests using the moment of inertia formula for a hollow cylinder and emphasizes the need to consider the caps at the top and bottom of the ball when calculating the total moment of inertia.
  • A third participant provides a visual description of the ball's structure, indicating how the solid part appears when viewed from different angles.
  • There is uncertainty expressed regarding the understanding of the equations and whether the moment of inertia for the caps needs to be included in the calculations.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the inclusion of the caps in the moment of inertia calculation, and there is some confusion regarding the equations and their application.

Contextual Notes

Participants have not fully clarified the assumptions regarding the geometry of the ball and the caps, nor have they resolved the mathematical steps necessary for calculating the total moment of inertia.

sushilshinge
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I want to calculate the torque required to rotate a ball.
1. Ball is solid having mass M kg.
2. Ball is bored through about its axis.
3. Ball is rotating about the axis XX

Please see attached file.
 

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You must find the moment of inertia of a hollow cylinder which is,
[tex]I=1/2 m ( r_i^2 + r_0^2)[/tex]
r_i and the r_0 are radial distances from centre.

Than the relationship between torque, moment of intertia and angular acceleration, which is,
[tex]T=I \alpha[/tex]

Now looking at the picture I am not sure if ur including those caps on the top and bottom. In which case you must find their moment of intertia and add it to the cylinder
 
Right side view is a section of a ball. The hatching part is a solid part of ball.When you will cut the ball in left view in middle then by looking left side it will look like in right view.
 
Not sure I completely understand what your saying. Are the equations what you are after? Just find the moment of inertia of the top and bottom parts, if indeed I am understanding you correctly
 

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