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Multiverse

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I have problem to see clearly the case of rotation of a body about a point with decreasing radius.this can be viewed as a body being rotated about a point with the help of a thread which passes through a hole in a disc and the thread is being pulled to apply a tension and gradually to decrease the length of the thread.I have attached a word doc. to have a clear pic. about it.It can seen that here that the instantaneous velocity has two components ,one perpendicular to the radius & other along radius. The tension is along the thread or radial.

there are some points to be noted.

1 .the tension being perpendicular cannot do any work on the perpendicular comp. of velocity & cannot change its magnitude.

2.there is no torque about the center as tension is radial. So, angular momentum should be conserved.

But the problem is angl. momen. is

as angu. momen. is constant so r*mv

Then if r decreases so then v

there are some points to be noted.

1 .the tension being perpendicular cannot do any work on the perpendicular comp. of velocity & cannot change its magnitude.

2.there is no torque about the center as tension is radial. So, angular momentum should be conserved.

But the problem is angl. momen. is

**r**X**p**. or " r*mv_{perpendicular}".as angu. momen. is constant so r*mv

_{perpendicular}should be constant.Then if r decreases so then v

_{perpendicular}must change. And it means that the perpendicular comp. of velocity changes ,which violate the 1st point.