- #1

Karol

- 1,380

- 22

## Homework Statement

I was told that I can use the rigid body angular momentum formula T=I[itex]\alpha[/itex]

Aroud 3 points: a fixed one (I assume the temporary center of rotation), or the center of mass or a point moving parallel to the c.m.

I have tested it with the case shown in the picture: a cylinder rotating on a rough surface, a steady force acting on it's center.

When calculating the angular acceleration [itex]\alpha[/itex] round the points A and C I get the same result, but when calculating around B-a different one, meaning the above is correct.

Why is that? the formula L=I[itex]\omega[/itex] is derived this way:

[tex]L=\sum_{n=1}^N L_n=\sum_{n=1}^N m_nv_n\cdot r_n=\sum_{n=1}^N m_nr^2_n \omega=I\omega[/tex]

So, I understand, in order to get the velocity of the particle correct, I have to calculate only round the stationary point of rotation. The formula T=I[itex]\alpha[/itex] is only the derivative of the former.

Can anyone explain a bit, and give a name of a book that explains this in detail, since some ordinary books talk only in general about this.