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Question

A particle of mass $m$ is projected from point $A$ with an initial velocity $\mathbf{v}_0$ perpendicular to line $O A$ and moves under a central force $\mathbf{F}$ along a semicircular path of diameter $O A$. Observing that $r=r_0 \cos \theta$ and using Eq. (12.27), show that the speed of the particle is $v=v_0 / \cos ^2 \theta$.

Solution

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A particle of mass m is projected from Point A with an initial velocity v0 perpendicular to line OA and moves under a central force F along a semicircular path of diameter OA.

Observing that $r = r_o \cos\theta$ and using Eq. (12.25),

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