A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$, where $k$ is a positive cons ant. If the particle's angular momentum is $L = 2mr^2 omega$, find the total energy of the particle in terms of $m$, $r$, and $k$.

Question

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$, where $k$ is a positive cons	ant. If the particle's angular momentum is $L = 2mr^2 omega$, find the total energy of the particle in terms of $m$, $r$, and $k$.

Accepted Answer

\frac{1}{2} m r^2 \omega^2 - \frac{k}{r}

Post Utme Ksu 2018 Physics Question 16

A particle of mass $m$ is moving in a circular orbit of radius $r$ under the influence of a central force given by $F(r) = -\frac{k}{r^2}$, where $k$ is a positive cons\tant. If the particle's angular momentum is $L = 2mr^2 omega$, find the total energy of the particle in terms of $m$, $r$, and $k$.

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