As we all know energy and mass are equivalent. When I burn wood a small amount of mass is converted to energy. In theory, I could convert energy to mass. This is not practically possible, but, if I understand it correctly, mathematically they are equivalent ($E=mc^2$). Mass, however, can be expre...

I tried to get the approximation for small angle of a simple pendulum using only $\sum \mathbf F = m\mathbf a$ and cartesian coordinates (that means only $x$'s and $y$'s, without $\theta$). After some derivatives I got the expression: $$a_x = \left(\frac{x}{L}\right)\left(\frac{v_x^2}{L} – g\righ...