Problem 1.186

A ball of mass $m$ is thrown at an angle $\alpha$ to the horizontal with the initial velocity $v_{0} .$ Find the time dependence of the magnitude of the ball's angular momentum vector relative to the point from which the ball is thrown. Find the angular momentum $M$ at the highest point of the trajectory if $m=130 \mathrm{~g}, \alpha=45^{\circ},$ and $v_{0}=$ $=25 \mathrm{~m} / \mathrm{s} .$ The air drag is to be neglected.

\begin{aligned} & \text { 1.186. } M=1 / 2 m g v_{0} t^{2} \cos \alpha ; \quad M=\left(m v_{0}^{3} / 2 g\right) \sin ^{2} \alpha \cos \alpha=\\ =& 37 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s} \end{aligned}

Laws of Conservation