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Laws of Conservation

Problem 1.188

A small ball of mass \(m\) suspended from the ceiling at a point \(O\) by a thread of length \(l\) moves along a horizontal circle with a constant angular velocity \(\omega .\) Relative to which points does the angular momentum M of the ball remain constant? Find the magnitude of the increment of the vector of the ball's angular momentum relative to the point \(O\) picked up during half a revolution.

Reveal Answer
 1.188. Relative to the centre of the circle. ∣ΔM∣=21−(g/ω2l)2mgl/ω\begin{aligned} &\text { 1.188. Relative to the centre of the circle. }\\ &|\Delta \mathbf{M}|=2 \sqrt{1-\left(g / \omega^{2} l\right)^{2}} m g l / \omega \end{aligned}
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