Conceptual Questions for Physics 310 (Theoretical Mechanics I)
Newton's Laws of Mechanics:
I) A body remains at rest or in uniform motion unless acted
upon by a force
II) A body is acted upon by a force in such a manner that the time
rate of change of momentum equals the force.
III) If two bodies exert forces on each other, these forces are
equal in magnitude and opposite in direction.
- Chapter 2
- 1 : Rewrite Newton's 2nd Law as a vector equation
using derivatives
- 2 : Explain how laws II and III lead to conservation
of momentum
- 3 : What is inertial mass ? What is gravitational mass ?
What is the equivalence principle ?
- 4 : What is an inertial frame of reference ?
- 5 : Is the earth an inertial frame of reference ?
Give an example of a physical effect related to your answer ?
- 6(a) : For air resistance when is the retarding
force proportional to v and when is it proportional to v^2
- 6(b) : How does the retarding force depend on the
cross sectional area and density of the medium ?
- 6(c) : What happens to the skin of the Concorde
aircraft as it passes the speed of sound ?
- 7 : What is the effect of air resistance
on the range of a projectile ? What is the effect of the
altitude dependence of the density of air ? What is
the effect of air resistance on the maximum height of a projectile ?
- 8 : What is the effect of air resistance
on the final velocity of a sky diver ? How does this result
depend on the initial velocity ?
- 9 : Sketch the trajectory of a charged
particle in a uniform magnetic field along the z direction.
Assume the initial velocity is in the y direction.
- 10 : Explain how rocket propulsion is related to
conservation of momentum
- 11 : Under what conditions does Newtonian mechanics
break down ?
- 12 : How did Wolfang Pauli deduce the existence
of the neutrino ?
- Chapter 3
- 1 : What differential equation describes
a simple harmonic oscillator (SHO) ? What are examples
of physical systems that can be modeled as SHOs ?
- 2 : What is the relation between
total mechanical energy and amplitude of oscillation
for an SHO ?
- 3 : How does the period of a SHO depend
on amplitude ?
- 4 : What is a Lissajous curve ? When is it closed ?
- 5 : What is phase space ? What is a phase diagram ?
- 6 : What is the shape of
the contours in the phase diagram for a simple harmonic
oscillator ? What are the contours in the phase diagram for
a damped simple harmonic oscillator ?
- 7 : What is the phase portrait for
overdamped motion ? How does it depend on the initial velocity ?
- 8 : What differential equation describes
a forced damped harmonic oscillator ? What do the
terms "transient" and "steady state" mean ?
- 9 : At what frequency does resonance occur ?
How does the resonant frequency depend on the amount of
damping ?
- 10 : What is Q ? How is Q related to the width
of the resonance curve and the amount of damping ?
- 11 : What is the
frequency where the kinetic energy is maximum in a forced
damped oscillator ? What is the frequency at which U is maximum
for a forced damped oscillator ? Why are they different ?
- 12 : What electrical circuit is the equivalent
of a SHO ? What circuit is the equivalent of a damped
simple harmonic oscillator ? What about a forced damped
harmonic oscillator ?
- 13 : What is a Fourier series ? What is a practical
application ?
- Chapter 4
- 1 : What is meant by "Chaos" ? How does this
differ from random ?
- 2 : Give an example of a physical system
which exhibits chaotic behaviour.
- 3 : Who was the mathematician/physicist
who first recognized chaos ? In what physical system ?
- 4 : What is the phase portrait of the Van der Pol
equation ?
- 5 : What differential equation describes the
plane pendulum
- 6 : What is meant by "hysteresis" and "jumps" ? When
does this occur for an oscillator ?
- 7 : What is a Poincare section ?
8 : What is the logistic equation ?
- 9 : What is period doubling/bifurcation ?
- 10 : What did Mitchell Feigenbaum discover
about the ratio Delta alpha_n/Delta alpha_n+1 ?
- 11 : What is meant by sensitivity to initial
conditions ?
- 12 : What is the Lyapunov exponent ? What does
it measure ?
- Chapter 5
- 1 : Why did Newton delay the publication of the Principia
by 20 years ?
- 2 : What is Newton's Law of Gravitation for point masses
and continuous distributions ?
- 3 : What is the relation between the gravitational field
and the gravitational force ?
- 4 : How is the gravitational potential defined ?
- 5 : What is Poisson's equation ? How is it related
to Gauss' Law ?
- 6 : What is an equipotential surface ?
- 7 : Are lines force perpindicular to or parallel
to equipotentials ?
8 : Explain qualitatively the origin of tides.
- 9 : Why are there two high tides a day ?
- 10 : The gravitational force of the sun on the earth
is 175 times larger than the force from the moon.
Why are tides primarily due to the interaction of
the earth and the moon ?
- Chapter 6
- 1 : What is Fermat's Principle ?
- 2 : What is Euler's Equation ?
- 3 : What is a geodesic ? What is a geodesic
on a sphere ?
- 4 : Explain the idea of Lagrange Multipliers.
Chapter 7
1 : What is Hamilton's Principle ?
2 : What are generalized coordinates ?
3 : What is the physical interpretation
of the Lagrange Multiplier term in the Euler-Lagrange equation
with constraints ?
4 : What is a holonomic constraint ?
5 : What are generalized momenta ?
6 : What is the Hamiltonian ?
7 : When is the Hamiltonian equal to the total energy ?
8 : What are the advantages of using the Lagrangian
and Hamiltonian formulations of mechanics compared to using
Newton's Laws directly ?
9 : What is Noether's Theorem ?
10 : What conserved quantity corresponds to rotational
symmetry of the Lagrangian ? Translational symmetry of the Lagrangian ?
Tom Browder
November 25, 1999