A particle with mass $m$ is moving with constant speed $v$ along a circular orbit (radius $r$).

The centripetal force $F=mfrac{v^2}{r}$ is provided by gravitation force from another mass $M=F/g$.

A string is connected from mass m to the origin then connected to mass $M$.

Because the force is always in the $hat{r}$ direction, so the angular momentum $vec{L}=m,vec{r} imes vec{v}$ is conserved. i.e. $L=mr^2omega$ is a constant.

For particle with mass m:

$ m frac{d^2r}{dt^2}=mfrac{dv}{dt}= m frac{v^2}{r}-Mg=frac{L^2}{mr^3}- Mg $

$ omega=frac{L}{mr^2}$

The following is a simulation of the above model.

You can change the mass M or the radius r with sliders.

The mass M also changed to keep the mass m in circular motion when you change r.

However, if you change mass M , the equilibrium condition will be broken.

Full screen applet or

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Creative Commons Attribution 2.5 Taiwan License
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