Physics 301
(Fall 1998)
Final Exam (December 14, 1998)
Name
1.
[25 points total]
A pendulum swings in the boxcar of a train as shown.
The mass of the bob
is m, and the length of the string is b.
The train car speeds up to the right with acceleration a.
A.
[10 points]
Find the Lagrangian for the bob.
Show your work.
B.
[15 points]
Use Lagrange’s method to find the equation of motion.
Show your work.
(Hint:
You should have one equation for
θ
.)
m
b
a
θ
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2.
[30 points total]
A thin plate, having radius R and
uniform areal density
σ
, is cut in half.
One of the
halves is then hung on the wall with a frictionless nail
that passes through the pivot point P, as shown.
A.
[10 points]
Find the moment of inertia of the half
plate about this pivot.
Show your work.
B.
[10 points]
Find the location of the center of mass of the half plate.
Show your work.
C.
[10 points]
Find the frequency of oscillation for small oscillations about pivot P.
Show
your work.
If you were not able to find answers to parts A or B above, explain how you
would
use your answers to find the frequency of small oscillations.
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 Fall '97
 GregoryFrancis
 Force, Mass, Earth’s center, e. b

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