JEE Main & Advanced Physics Two Dimensional Motion Centripetal Acceleration

(1) Acceleration acting on the object undergoing uniform circular motion is called centripetal acceleration.

(2) It always acts on the object along the radius towards the centre of the circular path.

(3) Magnitude of centripetal acceleration,  

\[a\,=\frac{{{v}^{2}}}{r}={{\omega }^{2}}r=4{{\pi }^{2}}{{n}^{2}}r=\frac{4{{\pi }^{2}}}{{{T}^{2}}}r\]   

(4) Direction of centripetal acceleration : It is always the same as that of \[\Delta \overrightarrow{\upsilon }\]. When \[\Delta t\] decreases, \[\Delta \theta \] also decreases. Due to which \[\Delta \vec{\upsilon }\] becomes more and more perpendicular to \[\overrightarrow{\upsilon }\]. When \[\Delta t\to 0,\] \[\Delta \overrightarrow{\upsilon }\] becomes perpendicular to the velocity vector. As the velocity vector of the particle at an instant acts along the tangent to the circular path, therefore \[\Delta \overrightarrow{\upsilon }\] and hence the centripetal acceleration vector acts along the radius of the circular path at that point and is directed towards the centre of the circular path.