What is the Angular Velocity at a Given Angle for a Given Angular Acceleration?

[seboastien]

Homework Statement

angular acceleration of line a= -2w^2 rad/s

when theta=pi/6, w= 10 rad/s

what is angular velocity when theta= pi/3?

Homework Equations

chain rule

The Attempt at a Solution

w= e^-2theta is my answer, but I know this is wrong

I know that this question is really easy, but I just don't know how to get it

 

[rock.freak667]

Well you should know that α= -2ω² means that dω/dt = -2ω²

which is an easily solvable DE once you 'separate the variables' i.e. put all the things with ω on one side and t on the other then integrate both sides.

 

[seboastien]

But then I end up with t=1/2w, how do I find the rest of the answer?

 

[seboastien]

Someone please help me!

 

[rock.freak667]

But then I end up with t=1/2w, how do I find the rest of the answer?

I now saw that you have ω and θ so forget my above post and replace α with ω*dω/dθ and integrate again. Do not forget the constant of integration which you can find with the conditions they gave you.

 

[seboastien]

Yes, that was my problem all along... I forgot to add the constant! Thanks.