Question

A particle starts from rest and moves along a circular path with constant tangential acceleration after one rotation ratio of centripetal acceleration to its tangential acceleration would be

Answer 1

nswers : (1)

Let the initial tangential acceleration of the point be “a”.

Let the radius of the circular path = R

Circumference of the circular path = 2πR

By using the third equation of motion: v2 = u2 + 2aS

We have initial velocity = u =0

acceleration = a ( dont get confused between the both a’s)

S = 2πR

from here we get v2 = 2 x a x 2πR = 4πRa

So velocity of the point after moving one complete rotation(2πR) = √4πRa

Now radial acceleration of the point after moving 1 complete rotation = v2/R = (√4πRa )2/R = 4πRa/R = 4πa

Since tangential acceleration was constant throughout the path from beginning so it is equal to a

Ratio = a / 4πa = 1/4π Answer