The sum of energy in a rotation

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Offline LB7

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The sum of energy in a rotation
« on: 03/06/2016 23:26:45 »
The study:

A force turns around the center O in a circle (dotted lines), the force keeps its angle with the radius (beta is constant = 30). The radius of the circle is 1. The force is 1. An external device gives the force F. It's easy to calculate the work needed to rotate the force from 0 (vertical) to 90 it is 0.5 from vertical to horizontal (rotate of 90).

Now, take the black arm. The black arm turns around the red point, but it takes the force F at the end and it must increase its length if I want the force F turns around the center O.

Now the work is  :

There is a difference !

Maybe I need to do that:

But there is always a difference:

2*cos(x)*sin(x+pi/6)-2*sin(x)*cos(x+pi/6) dx from pi/4 to 0

I found my error, it was the length in the integration. The sum of energy is 0.
« Last Edit: 04/06/2016 13:24:01 by LB7 »