Physics 325 Homework 10  Fall 2010
Due: Thursday 11 November at 11:15 am
Please note that you have only two extra days in which to complete this
assignment as the solutions will be posted at noon on Saturday 14 Nov.
1)
[10 points]
Taylor: Problem 7.52, p 291. Consider a mass
m
that hangs from a string,
the other end of which is wound several times around a wheel (radius
R
, moment of
inertia
I
) mounted on a frictionless horizontal axle. Use as coordinates for the mass
and the wheel
x
, the distance fallen by the mass, and
φ
, the angle through which the
wheel has turned (both measured from some convenient reference position).
a)
Write down the modified Lagrange equations for these two variables and solve
them (together with the constraint equation) for
!!
x
, the second time derivative of
φ
“
φ
double dot”,
and the Lagrange multiplier,
λ
.
b)
Write down Newton’s second law for the mass and wheel, and use these to check
your answers for
!!
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 Fall '08
 Staff
 mechanics, Force, Mass, Work, Lagrangian mechanics, frictionless horizontal axle

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