What Torque is Needed to Rotate a Solid Bored Ball?

AI Thread Summary
To calculate the torque needed to rotate a solid bored ball, the moment of inertia must first be determined using the formula I=1/2 m (r_i^2 + r_0^2), where r_i and r_0 are the inner and outer radial distances. The relationship between torque (T), moment of inertia (I), and angular acceleration (α) is expressed as T=Iα. There is uncertainty regarding whether to include the caps at the top and bottom of the ball in the moment of inertia calculation. If included, the moment of inertia of these caps must be calculated and added to that of the hollow cylinder. Understanding and applying these equations is essential for accurate torque calculation.
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

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

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

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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