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rdlcsh
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Homework Statement
A thin rod of length 1.4m and mass .2kg is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 7.84 rad/s. Neglecting friction and air resistance, find how far above that position the center of mass rises.
m = .2 kg
l = 1.4 m
max angular velocity = 7.84 rad/s
I've figured out:
moment of inertia = .130666
max kinetic energy = 4.0157 J
Homework Equations
Work = integral of the torque from (theta-0 to theta-max)
tourqe = rF*sin(theta) = rmg*sin(theta)
tourqe = I(angular acceleration)
The Attempt at a Solution
I've tried integrating both tourqe equations above as well as integrating the second one subtracted from the first one. But i usually end up with something like:
sin(theta) = a number larger than 1
I think I am just integrating the wrong thing. I know this could probably be done with the conservation of engergy, but when I try that, I end up with a height that is greater than the lengh of the rod.
Thanks for any help!