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Lets suppose we have 2 point masses one fixed and imoveable the other rotateing in a perfect circle around the first imoveable one with constant speed.

Regardless of vich force is keeping the rotating mass on its circular orbit.

It may be a string or gravitational force or whatever.

The velocity of the rotating mass will allways be tangential to the circle the mass follows but the velocity vector intensity is the same as stated above (constant speed).

Now lets pull the rotating mass closer to the fixed mass, shorten the radius.

The conservation of angular momentum states that the the tangential spped of the rotating object should increase

If we aply a force orthogonal to the velocity vector to shorten the radius then this force could never ever change the intensity of the velocity.

Yet the conservation of angular momentum states different.

What is going on