What Causes Discrepancies in Calculating Initial Angular Velocity?

[AlexH]

Homework Statement

A wheel rotates with a constant angular acceleration of π rad/s^2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is its angular velocity at the beginning of the time interval?

Homework Equations

angle displacement = (initial rotational velocity * time) + 1/2(rotational acceleration)time^2
rotational velocity = rotational acceleration * time
rotational velocity^2 = (initial rot. velocity^2) + 2(rotational acceleration)(angle displacement)

The Attempt at a Solution

When plugging in the values into the third equation, I'm able to solve the problem and get the correct answer (π*sqrt2).

But I'm wondering what's wrong with my other way of doing it.
I tried solving for the time by plugging in the final velocity and acceleration into the 2nd equation (2π = π*t), which gives t = 2.
Then I plugged the values into the first equation to try to solve for the initial angular velocity (π = (initial rotational velocity x 2) + 1/2(π)2^2
But that didn't work out. Is there a reason why?

Thanks for any help!

 

[Orodruin]

Your formula for the rotational velocity is not complete. You have ignored the initial rotational velocity in it.

 

[AlexH]

Your formula for the rotational velocity is not complete. You have ignored the initial rotational velocity in it.

I see, thanks!