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## Homework Statement

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.

## Homework Equations

[itex]a=\sqrt{a_{r}^2+a_{t}^2}[/itex]

[itex]a_{r}=ω^2r[/itex]

[itex]a_{t}=αr[/itex]

## The Attempt at a Solution

Using those equations, I find an expression for the total acceleration:

[itex]a=r\sqrt{ω^4+α^2}[/itex]

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.

LovePhys