There is a problem in Halliday, Resnick, and Walker that asks for the
deviation from vertical that a plumb bob experiences when it is hung at a
latitude of 40 degrees. I consider the pendulum to be composed of two
component pendula, one that is perpendicular to the rotational surface,
which requires taking the sine of the weight and the tension. The other
component is parallel to the surface and has no effect. If the Earth did
not rotate, this component pendulum would have a weight pulling down of w
sin(theta) and a tension pulling up of T sin(theta), where theta is the
latitude. In the presence of rotation, the weight term remains the same
and the centripetal term comes from the additional tension force that is
created as the pendulum moves outward by the deviation angle. I calculate
an angle of 0.23 degrees, while the back of the book lists 0.09 degrees.
This is Problem # 71 in Chapter 5 of the previous edition. The one with
the streaming lights on the front.
Tom McCarthy
Saint Edward's School
1895 St. Edward's Drive
Vero Beach, FL 32963
561-231-4136
Physics and Astronomy