Dynamics of circular motion
Dynamical criterion of circular motion
An object moves in uniform circular motion if and only if the net force vector has a radial component whose magnitude is equal to the centripetal force. If the net force also has a tangential component, the acceleration will have a tangential component and the motion will be non-uniform circular motion.
|
|
The net force vector acting on the object can be resolved into radial and tangential components: \[\sum{\mathbf{F}} = \sum{\mathbf{F}_r} + \sum{\mathbf{F}_{\mathrm{t}}}.\] \[\left|\sum{\mathbf{F}_r}\right| = m \left|\mathbf{a}_r\right| = m \frac{v^2}{r} = m \omega^2 r.\] The tangential component of the net force vector will cause tangential acceleration: |
