Non-Uniform Circular Motion


Non-uniform circular motion is any case in which an object moving in a circular path has a varying speed e.g. a vertical pendulum ,the pendulum’s mass swings in a semicircle in which its trip up slows down to 0 m/s and comes back down.
Solving applications dealing with non-uniform circular motion involves force analysis. With uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration.
In uniform circular motion, total acceleration of an object in a circular path is equal to the radial acceleration. Due to the presence of tangential acceleration in non uniform circular motion, that does not hold true anymore. To find the total acceleration of an object in non uniform circular, find the vector sum of the tangential acceleration and the radial acceleration.
a=(ar2+at2)0.5


Radial acceleration is always equal to v2/r. The tangential acceleration is simply the derivative of the velocity at the given point.
at=dv/dt