What Torque is Needed to Rotate a Solid Bored Ball?

[sushilshinge]

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.

 

[crissyb1988]

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

 

[sushilshinge]

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.

 

[crissyb1988]

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

 

[PJC01]

To calculate the torque required to rotate a ball, we first need to understand the concept of torque. Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance from the axis of rotation.

In this scenario, the ball is solid with a mass of M kg and is rotating about the axis XX. Since the ball is bored through about its axis, we can assume that the axis of rotation is passing through the center of the ball. This means that the distance from the axis of rotation to any point on the ball is equal to the radius of the ball.

To calculate the torque, we need to know the force applied to the ball. This force can be calculated using Newton's Second Law, which states that force is equal to mass multiplied by acceleration (F=ma). Since the ball is rotating at a constant speed, the acceleration is zero, therefore the force applied is also zero.

Without any external force, the ball will not rotate. Therefore, we can conclude that the torque required to rotate the ball is also zero. This is because torque is directly proportional to force and since there is no force, there is no torque.

In summary, the torque required to rotate a ball depends on the force applied to the ball, which in this case is zero. Therefore, the torque required to rotate the ball is also zero.