Is angular momentum and mechanical energy is conserved or not

A ball is aatached to a string that is attached to a pole . when the ball is hit, the string wraps around the pole and the ball spiral inwards sliding on frictionless surface . Neglecting air resistance .

I think mechanical energy is conservesd as there is no friction and I also think that angular momrntum about centre of pole is conserved when ball swings around the pole .

But in my book it is written as angular momentum about centre of pole is notconserved when ball swings around the pole .

I could not understand this .

You need to consider the following given that the force on the ball is due to the tension in the string.

Does the ball have a component of its displacement in the direction of the tension in the string? If it does then work is done on the ball and so the ball's kinetic energy is not constant whilst if not then no work is done on the ball and then kinetic energy is conserved.

Is there a torque on the ball about the centre of the pole due to the tension in the string?
If there is a torque the angular momentum is not conserved but if the torque is zero then angular momentum is conserved.

• I don't think here there is tension then why angular momentum is not conserved – search Apr 22 '17 at 17:55
• If there was no tension the ball would move in a straight line. – Farcher Apr 22 '17 at 18:48