Physics 311
Problem Set 1
Due Thursday, Sept. 11

1. State the authors, titles, publishers, and dates of publication of two books on the reserve shelf for Physics 311 in the Physics Library. Write a paragraph or two on each book giving your first impressions of it (based, for example, on reading the preface, the table of contents, a couple of chapters, etc.).
2. Dimensions of physical constants. Determine the dimensions of the following physical constants in the -class: (Planck's constant), (Boltzmann's constant), (permittivity of free space), (permeability of free space), G (gravitational constant), c (speed of light), e (the electron charge).
3. Period of a pendulum. Derive an expression for the period of small oscillations of a pendulum of mass m, with a momentum of inertia I about its pivot point and a distance l between the pivot and the center of mass. Do this by drawing an accurate free body diagram and then apply Newton's Second Law for rotational motion ( , with I the moment of inertia, the angular acceleration, and the net torque). In class I argued from dimensional considerations that . What is the function ?
4. Oscillations of a water drop. Use dimensional analysis to determine how the oscillation frequency of a water drop of radius R scales with various physical quantities. You may assume that gravitational effects are negligible. How would the oscillation frequencies of two drops of the same fluid compare if the radius of the first is 3 times that of the second?