Angular Acceleration and wheel revolution

AI Thread Summary
A wheel accelerates from rest to 59 rad/s at an acceleration of 29 rad/s², prompting a discussion on how to calculate the total revolutions during this acceleration. The participants express confusion about relating angular displacement, angular velocity, and angular acceleration without time. It is suggested that the initial and final velocities, along with acceleration, can be used to derive time. The analogy to linear motion equations is highlighted, but the need for a formula that directly connects angular variables without time is emphasized. Ultimately, the conversation centers on finding a solution to the problem using the given parameters.
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Homework Statement



A wheel accelerates from rest to 59 rad/s at a rate of 29 rad/s². How many revolutions the wheel turned while accelerating?

Homework Equations

The Attempt at a Solution



I'm confused, I suck at this kind of problem. I got change in angular velocity which would be 59rad/s, and I got that the angular acceleration would be 29 rad/s². What equation relates all three? All equations I know relate them using time, but I got no time there.
 
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The equation you are looking for is an EXACT analog of the equation for linear motion, s=(1/2)*a*t^2. Does that help?
 
Not really. See that would translate into angular motion as this:

Angular Displacement = 1/2*Angular Acceleration*Time²

And since I got no time, that equation is useless. I need an equation that somehow relates ONLY angular displacement to angular velocity and angular acceleration

Unless I'm missing a way to get the time from the given data...
 
Well, you know the initial velocity, the final velocity and the acceleration. Could that give you a time?
 
...could it?
 
I would say that if I accelerate from 0 to 10 m/sec at an acceleration of 10 m/sec^2, then the time it takes is 1 sec.
 

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