Pendulum Clock in Non-inertial Frame
المؤلف:
Sidney B. Cahn Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 25
1-8-2016
1334
Pendulum Clock in Non-inertial Frame
An off-duty physicist designs a pendulum clock for use on a gravity-free spacecraft. The mechanism is a simple pendulum (mass m at the end of a massless rod of length l) hung from a pivot, about which it can swing
Figure 1.1
in a plane. To provide artificial gravity, the pivot is forced to rotate at a frequency ω in a circle of radius R in the same plane as the pendulum arm (see Figure 1.1). Show that this succeeds, i.e., that the possible motions θ(t) of this pendulum are identical to the motions θ(t) of a simple pendulum in a uniform gravitational field of strength g = ω2R, not just for small oscillations, but for any amplitude, and for any length l, even l > R.
SOLUTION
Calculate the Lagrangian of the mass m and derive the equation of motion for θ(t) (see Figure 1.2). Start with the equations for the x and y positions of the mass
and compose
Figure 1.2
Applying Lagrange’s equations gives
which, for g = ω2R, corresponds, as required, to the equation of motion for a pendulum 
in a uniform gravitational field.
الاكثر قراءة في مواضيع اخرى
اخر الاخبار
اخبار العتبة العباسية المقدسة
