Conservation of Energy for a rotating Rod

AI Thread Summary
The discussion centers on understanding the potential energy of a uniform rotating rod, specifically why it is expressed as MgL/2. The center of mass of the rod is located at L/2, which is crucial for calculating potential energy. The torque from gravity is also discussed, noting that it varies with the angle of the rod. The relationship between height and the angle is clarified, leading to the conclusion that potential energy can be derived from mgh, where h is L/2. Overall, the key takeaway is the importance of the center of mass in determining potential energy and torque for a rotating rod.
AROD
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Homework Statement


rod%20problem.jpg

Homework Equations



Rotational Kinetic Energy = 1/2*I*w^2

The Attempt at a Solution



I was just wondering if someone explain to me why the potential energy is MgL/2 ?

Is this not the same for the torque from gravity?
 
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As the hint in a) states, you can neglect the mass m. And since the mass M is uniform, you can presume all its weight is in the center, hence MgL/2
 
Because the rod's center of mass is placed at L/2 over the ground.

Edit: oops, already answered :)
 
AROD said:
I was just wondering if someone explain to me why the potential energy is MgL/2 ?
The rod is uniform. Where is its center of mass?
Is this not the same for the torque from gravity?
The torque from gravity about the pivot point depends upon the angle of the rod.

Edit: Already answered twice!
 
ok so then its just mgh with h = L/2 . that makes sense

then as it tips the hypotoneuse would be L/2, and the height would be this times the cos of theta.

thanks
 

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