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Laws of Conservation

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.

Reveal Answer
 1.186. M=1/2mgv0t2cos⁡α;M=(mv03/2g)sin⁡2αcos⁡α==37 kg⋅m2/s\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}
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