Angular Velocity of a pivoting rod

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SUMMARY

The discussion centers on calculating the angular velocity of a uniform rod, 5.8 meters long and weighing 10 kg, pivoted at its center with a 5.15 kg weight attached at one end. The rod is released from a 37-degree angle. The initial calculations provided an angular acceleration of 1.6295 rad/s², but the user struggled to derive the correct angular velocity when the rod is vertical. Key equations referenced include the conservation of energy and the relationship between angular velocity and tangential velocity.

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Homework Statement


A uniform rod 5.8m long weighing 10kg is pivoted at its center and a small weight of mass 5.15 kg is rigidly attached to one end. You may neglect the size of the weight and assume it is located right at the end of the rod. It is held at a 37 degree angle at rest, then released.
What is the angular velocity when the rod is vertical?

Homework Equations


After some work, I earlier solved that angular acceleration at it's release point is 1.6295 Don't know if that will be needed or not...
Angular Velocity = Tangential Velocity /R
VF^2 = VI^2 + 2A (X1-Xf)

The Attempt at a Solution


I dared to hope I could do this on my first try, but was disappointed. (Again.)
5.8/2 = 2.9, so radius = 2.9
sin37 2.9 = 1.745
2.9-1.745 =1.1547 m of fall

VF^2 = 0 + 2 (9.81) (1.1547)
VF^2 = 22.65
VF = 4.76

4.76 / 2.9 = 1.64
It looks so right... but is so wrong. *sigh*
 
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Hi TG3! :smile:
TG3 said:
A uniform rod 5.8m long weighing 10kg is pivoted at its center and a small weight of mass 5.15 kg is rigidly attached to one end. You may neglect the size of the weight and assume it is located right at the end of the rod. It is held at a 37 degree angle at rest, then released.
What is the angular velocity when the rod is vertical?

VF^2 = VI^2 + 2A (X1-Xf) …

Sorry, not following your proof at all :confused:

using conservation of energy is right :smile:

but what's happened to the mass, and the moment of inertia ?
 

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