# Acceleration in non-uniform circular motion

• nashsth

#### nashsth

In a non-uniform circular motion (for example a pendulum), can the centripetal/radial acceleration ever be 0? Likewise, can the tangential acceleration ever be 0?

The centripetal acceleration occurs because of the centripetal force, which causes the body (in the example of the pendulum, the bob is the body) to continue moving in its path. So if the centripetal acceleration is 0, then doesn't that imply that the centripetal force is 0, which means that the object would stop going in a circular path? So is it correct to say that the centripetal acceleration is never 0 in a non-uniform circular motion?

As for the tangential acceleration, it is caused by a change in speed of the body. So, in the pendulum example, since the bob has 0 speed at its peak positions, would it have 0 tangential acceleration only at its peak positions?

NOTE: Peak position = the maximum position that a pendulum will attain before swinging down again.

I think it's the other way around. Tangential acceleration is maximal at the peak positions and zero at the base position, while centripetal acceleration is zero at the peak positions and maximal at the base. Your reasoning about centripetal acceleration is fine, but doesn't apply when the linear velocity is zero - ie at the peaks - because if the bob remained in that position it would not move away from the circle.