Calculate the angular velocity and angular acceleration (pendulum)

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The discussion focuses on calculating the angular velocity and angular acceleration of a simple pendulum with a tension of 7.5N at an angle of 30 degrees. Participants evaluate the correctness of the calculations presented, noting that while the overall approach seems reasonable, specific numerical checks were not performed. The importance of applying the correct equations for angular motion in pendulums is emphasized. The conversation highlights the need for accuracy in physics problems, particularly in homework settings. Overall, the thread underscores the significance of verifying calculations in angular dynamics.
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Homework Statement


13.53 The tension in the sting of the simple pendulum is 7.5N when θ=30deg.
Calculate the angular velocity and angular acceleration of the string at this instant.
Fig P13_53.jpg

Homework Equations

The Attempt at a Solution



Pytels_Dynamics079.jpg


Is this correct?
 
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Looks reasonable overall. Did not check the explicit numbers.
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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