A turntable is rotating at a constant angular velocity of ω = 4.0 rad/s in the direction of a clockwise fashion. There is a ten-cent coin on the turntable, at a distance of 5 cm from the axis of rotation.
Consider the time interval during which the turntable is accelerated initially from rest to its final angular velocity (ωf = 4.0 rad/s) . This is achieved with a constant angular acceleration (α) for 0.5 s.
Find an expression for the magnitude of total acceleration of the coin in terms of α and ω and use this to determine the maximum total acceleration experienced by the coin.
The Attempt at a Solution
Using those equations, I find an expression for the total acceleration:
I don't understand why the problem is asking for a maximum total acceleration. I am already given the values of r, ω, and α, can I just substitute them in to find the answer? Another thing that came into my mind when the word "maximum" pops up is finding the derivative of a function of a(t) with respect to time, but apparently I do not have that function here...
Any help would be greatly appreciated.