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

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Homework Help Overview

The discussion revolves around a problem involving angular velocity and angular acceleration, specifically focusing on the relationship between angular acceleration and angular velocity at different angles. The original poster presents a scenario with given values for angular acceleration and initial angular velocity, seeking to determine the angular velocity at a specified angle.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the differential equation derived from the angular acceleration expression, with some suggesting the separation of variables as a method to solve it. Questions arise regarding the integration process and the handling of constants of integration.

Discussion Status

Participants are actively engaging with the problem, exploring different methods to approach the solution. Some guidance has been offered regarding the integration of the differential equation, and there is acknowledgment of the importance of including constants of integration. However, no consensus or final solution has been reached.

Contextual Notes

There is a mention of specific initial conditions and values provided in the problem, which may influence the integration process. The discussion reflects a learning environment where assumptions and methods are being questioned and clarified.

seboastien
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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
 
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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.
 
But then I end up with t=1/2w, how do I find the rest of the answer?
 
Someone please help me!
 
seboastien said:
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.
 
Yes, that was my problem all along... I forgot to add the constant! Thanks.
 

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