An object with a mass m moves in a force region characterized by the potential energy function
$V(x, y, z) = a(x^2 + y^2 + z^2) + \frac{b}{x^2 + y^2 + z^2}$
(a) Calculate the force components $F_x$, $F_y$, and $F_z$ in Cartesian coordinates.
(b) Calculate the force components $F_r$, $F_\theta$, and $F_\phi$ in spherical coordinates.
(c) Calculate the torque $\vec{\tau} = \vec{r} \times \vec{F}$, the angular momentum $\vec{L} = \vec{r} \times m\vec{v}$ in Cartesian coordinates.
(d) Calculate the torque and the angular momentum in spherical polar coordinates.
(e) Prove if the total energy $E = K + V$ is constant or not.
(f) Is the angular momentum conserved? Prove your answer!
