Angular acceleration of a computer disk drive

[elsternj]

Homework Statement

A computer disk drive is turned on starting from rest and has constant angular acceleration.
If it took 0.640s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?

Homework Equations

$$\theta$$=$$\theta$$_i+$$\omega$$_i1/2$$\alpha$$t²
$$\omega$$=+$$\alpha$$t

The Attempt at a Solution

Okay I looked this question up on these forums and found it, and what people were saying to do was just not working so see if you can steer me in the right direction.

$$\theta$$=$$\theta$$_i+$$\omega$$_i1/2$$\alpha$$t²

12.56(rads) = 1/2$$\alpha$$(.64)²
solve that for $$\alpha$$
and you get $$\alpha$$ =61.3 (now i know this acceleration is wrong because it's supposed to be 5.26)

i would then put the acceleration in a new equation and solve for 6.28 rads but the acceleration isn't even right. why?

 

[RTW69]

It takes .64 seconds for the second revolution only. Break the problem into 2 sections starting with the second revolution you will end up with 2 unknowns. Now focus on the first revolution it will also have 2 unknowns but the final angular velocity for the first revolution will be the initial angular velocity for the second revolution. You can solve for the angular acceleration which is indeed 5.26/s^2. Plug that value into the equation for the first revolution and you are there.

 

[elsternj]

I am still feeling a little lost on this one. I can't find the acceleration because I need the initial velocity during the second rotation. I can't find the final velocity of the first rotation because i don't know the acceleration. I need a little more guidance with this one

 

[RTW69]

Start with the second revolution: you know time and 2Pi radians you don't know initial angular velocity or angular acceleration. So you have got an equation with 2 unknowns in it. You need another equation. Look at the first revolution. You know it travels 2pi, it's initial angular velocity is 0. But you don't know final angular velocity or angular acceleration. BUT the final angular velocity of the first revolution is the initial angular velocity for the second revolution. Now you have one equation with one unknown, the angular acceleration. You can use that value to find the time of the first revolution.