PHY820 Homework Set 1
1. [5 pts] A string is wrapped around a uniform homogeneous cylinder whose radius is
r and mass is m. The free end of the string is tied to the ceiling and the cylinder is
allowe
PHY820 Homework Set 2
1. [10 pts] A smooth wedge of mass M has a triangular cross section with a side inclined
at an angle to the horizontal base. The wedge can slide without friction along
a horizont
PHY820 Homework Set 3
1. [5 pts] Goldstein, Problem 1-10.
2. [5 pts] Two particles, characterized by charge q1 and q2 , respectively, and by mass of
m1 and m2 , move under the inuence of each other in
PHY820 Homework Set 4
1. [5 pts] Use the Lagranges equations, in combination with the Hamiltons principle, to
nd the shortest curve joining two arbitrary points on a cylindrical surface of radius
R. N
PHY820 Homework Set 5
1. [5 pts] Goldstein, Problem 2.2. Use the Noethers theorem and consider invariance
under the transformation ri ri = ri + n ri , where n is the direction vector for
the axis of r
PHY820 Homework Set 6
1. [10 pts] An exam problem: Discuss the 2-dimensional motion of a particle moving
in an attractive central-force described by the force law f (r) = k/r , where k is
positive and
PHY820 Homework Set 7
1. [5 pts] Goldstein, Problem 3.18. Use of the Runge-Lenz vector can be benecial.
2. [10 pts] Goldstein, Problem 3.31.
3. [5 pts] A proton of energy 4 MeV scatters o a second pro
PHY820 Homework Set 8
1. [5 pts] Goldstein, Problem 4-6.
2. [5 pts] Goldstein, Problem 4-14.
3. [5 pts] Goldstein, Problem 4-18.
4. [5 pts] Goldstein, Problem 4-21. Be concerned with the eects of unif
PHY820 Homework Set 9
1. [5 pts] Goldstein, Problem 4-21. Be concerned with the eects of uniform local gravity
and Coriolis force only. When the ball is dropped from rest, it is dropped while at
rest
PHY820 Homework Set 10
1. [5 pts] Goldstein, Problem 5-14.
2. [10 pts] Goldstein, Problem 5-16.
3. [10 pts] Goldstein, Problem 5-17. Note that there are two rotations here at play for
the cone. The an
PHY820 Homework Set 11
1. [5 pts] Goldstein, Problem 5-29.
2. [10 pts] (a) Within the Lagrangian approach to rotation, use conservation laws to
arrive at analytical solutions for the Euler angles as a
PHY820 Homework Set 12
1. [10 pts] Goldstein, Problem 6-4.
2. [10 pts] A thin hoop of radius R and mass M oscillates in its own plane hanging from
a single xed point on its circumference. Moving along
PHY820 Homework Set 13
1. [10 pts] For the system in problem 6-12 in Goldstein, determine the particle positions
as a function of time, if, at t = 0, (a) the displacements and the velocity of the seco
PHY820 Homework Set 14
1. [5 pts] Goldstein, Problem 8-14.
2. [10 pts] An exam problem: An ideally conductive square
loop can rotate around its side placed on the z -axis, as
shown, within a constant