What is the angular acceleration of an arm

AI Thread Summary
The discussion revolves around calculating the angular acceleration of an arm when the angle theta is 45 degrees, with a linear velocity of 2 m/s. The user has determined the length of side r to be approximately 579.555 mm using the law of sines. There is uncertainty about how to apply the laws of cosines or sines to find the time derivative of theta. A hint suggests that the velocity indicates how quickly the long side is increasing, and emphasizes the need to express the closed loop vectorially. The solution requires taking the time derivative of the angular orientation derived from the vector components.
Dusty912
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Homework Statement


what is the angular acceleration of the arm when theta equals 45 degrees.
v=2 m/s
picture is attached

Homework Equations


law of sites
law of cosines

The Attempt at a Solution


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so I used the law of sines to resolve side r as being 579.555 mm
now I now I need to take time derivative of theta somewhere using law of cosine or sines but I'm not really sure which one. also I don't know how to relate the 2 m/s to the problem
 

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Hint: The velocity is telling you how fast the long side is increasing.
 
Write the vector expression describing the closed loop. Solve this for the angular orientation of the arm (it will appear in the vector components). Take the time derivative of that result.
 
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