Angular acceleration of a bar on a hinge

AI Thread Summary
To determine the angle in radians that a bar on a hinge turns in the first 4 seconds, the angular acceleration given by α = (10 + 6t) rad/s² must be integrated twice with respect to time. The first integration yields angular velocity, and the second integration provides angular displacement. It is important to apply the appropriate constants of integration or boundary conditions, although they may not significantly affect this specific problem. The process involves calculating the definite integrals over the time interval from 0 to 4 seconds. The final result will give the total angular displacement of the bar during that time.
mickellowery
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Homework Statement


A bar on a hinge starts from rest and rotates with \alpha=(10+6t) rad/s2 t is in seconds. Determine the angle in radians the bar turns in the first 4 seconds.


Homework Equations


I'm a little stumped how to get this one started. I assume i need to get it from angular acceleration to angular displacement, but I'm not exactly sure how to do that. So do I have to integrate it with respect to time twice?


The Attempt at a Solution

 
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That's right. Remember to use constants of integration/ boundary conditions in general (although it should make no difference in this case).
 

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