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Problem 49 Easy Difficulty

The square frame is composed of four equal lengths of uniform slender rod, and the ball attachment at $O$ is suspended in a socket (not shown). Beginning from the position shown, the assembly is rotated $45^{\circ}$ about axis $A-A$ and released. Determine the initial angular acceleration of the frame. Repeat for a $45^{\circ}$ rotation about axis $B-B .$ Neglect the small mass, offset, and friction of the ball.

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Video Transcript

using parallel access to them. So I'm using the paddle access to REM the moment off Inner CIA about access A can be written like this. So this is the equation. And on solving this, we get i e. A is equal to this Now, in this next tip, I just calculated for I b B. So I just write the equation, using the pallor access to them. So in the next step, I will solve this equation. So this equation is very important equation. So on solving we get m b squared by tool plus seven m b squared by six plus 13 MV squared by tool and on solving this, we get this value as final for I B B. No solving I A into Alfa is equal to four mg in Toby by two into sign 45 degrees so it can be further written like this. So in the next step, I will solve it. So I just put all the data that I calculated earlier as well as given in the problem. So Alfa is coming as this. So this is the value off Alfa now solving I BB Alfa is equal to four mg in Toby by toe into sign 45 degree so it can be written like this further. And in the next step, we can write it like this. So Alpha is coming us This. So this is the final value off Alfa.