Horizontal Circular Motion of Mass on a Table

A particle with mass m is moving with constant speed v along a circular orbit (radius r ). The centripetal force $ F=\frac{mv^2}{r} $ is provided by gravitation force from another mass $M=\frac{F}{g} $. A string is connected from mass m to the origin then connected to mass M . Because the force is always in the r direction, so the angular momentum $ \widehat{L} = m\widehat{r} \widehat{v} $ is conserved. i.e. $L=mr^2\omega $ is a constant. For particle with mass m:

$m \frac{d^2r}{dt^2}=m\frac{dv}{dt}=mv^2r−Mg=\frac{L^2}{mr^3}−Mg $

$ \omega = Lmr^2 $

Controls

You can change the hang mass M or the on the table 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.