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
allowed to fall, see the gure, starting from rest. As the str
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 horizontal support. Placed on the side of the wedge is a mass m
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 an external uniform electric
eld E . Examine the Lagra
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. Note: You can select coordinates from the cylindrical sy
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 rotation and is an innitesimally small angle of rotation
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 3 > > 2.
(a) Write down the equations of motion in pol
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 proton at rest. One proton
comes o at an angle of 30 in th
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 uniform local gravity
and Coriolis force only. When the bal
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 relative to the surface of Earth.
2. [5 pts] Goldstein,
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 angular velocities add up as vectors.
4. [5 pts] A spool
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 function of time, of an axially
symmetric body precess
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 the hoop, without friction, is
a small bead also of ma
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 second
particle are zero while the rst particle moves at a
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 uniform magnetic eld B along
the x-axis. The loops side