Question in a book:
A ball of $mass = 0.5kg$ is attached to the end of an inelastic string of length $L=0.5m$. The other end of the string is fixed. The ball is made to move on a horizontal circular path about the vertical axis through the fixed end of the string. The maximum tension that the string can bear is 324 N. The maximum possible angular velocity of the ball is 36 rad/s, the acceleration of the ball along the string is?.
Since the string is inelastic acceleration along the string is zero.
My problem with the solution:
Why on the earth would it be zero. If the ball is rotating with $\omega$ then shouldn't the centripetal acceleration which is along the string directed towards the center be $r\omega^2$? But it isn't mentioned in the problem with what $\omega$ the string is rotating. Then how to go about solving the problem?
PS: I am a physics tutor for 11th and 12th grades.