Rotational Motion and torque problem

[Alche]

1)The torque of the weight of anybody about any vertical axis is 0. Is it always true?

2)A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?

3) When several forces acts on a particle we take the torque of the resultant force. Is this result valid for the force acting on different particles of a body in such a way that their lines of action intersect at a common point ?

4)In pure rolling angular velocity is independent of the distance r from the axis of rotation. Why ?

 

[Eynstone]

1. Not unless the axis passes through the centre of mass.
2.yes
3.yes
4.The angle subtended doesn't depend on r & hence neither does the angular velocity.

 

[Alche]

1. Not unless the axis passes through the centre of mass.
2.yes
3.yes
4.The angle subtended doesn't depend on r & hence neither does the angular velocity.

Can you tell which point has vertical velocity for second question

 

[Ketman]

2)A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?

Suppose the sphere is rolling to the left. Draw a vertical line through the centre. Every point on the sphere to the right of the line is moving upward, every point to the left is moving downward. The only points on the surface that have zero vertical velocity are the point in contact with the ground, and the point directly opposite (the highest point on the surface). Edit: My bad. I should have said, any point along the vertical line will have no vertical velocity, not just the points at the extreme ends of the line.