Quick help with NUCM of a disc

[dsimpson]

Homework Statement

a disc drive at rest is powered up and accelerates according to alpha=alpha(i)sin(bt). this lasts for 1.66 seconds after which it no longer accelerates. alpha(i)=506 rad/s^2 b=1.89 radius of disc=3.9cm. After the disc is done spinning up what is the centripetal acceleration of the edge of the disc.

I take this to mean the acceleration at the time of 1.66 because the answer isn't zero. Don't i just plug the time into my equation?

 

[Soveraign]

Centripetal acceleration is acceleration directed towards the center of circular motion. So this is usually

$$a_c=-\omega^2 r$$

or
$$a_c=-\frac{v^2}{r}$$.

In either case you need to know how fast the disc is rotating (and its radius). So how would you determine how fast the disc is turning after 1.66 seconds?

 

[tomcue]

Yes, you are correct. To find the centripetal acceleration at the time of 1.66 seconds, you can plug in the given values of alpha(i), b, and the radius of the disc into the equation for centripetal acceleration, which is a = v^2/r. However, since the velocity is not given in the problem, you will need to calculate it first using the given information about the acceleration. Once you have the velocity, you can then plug it into the equation to find the centripetal acceleration at 1.66 seconds.