Introduction to Classical Mechanics · Problem 9.12

Angular momentum, Part II (General L) — Morin

Physics — Mechanics · circular-pendulum

Problem

Consider a pendulum made of a massless rod of length ℓ\ell with a point mass mm on the end. Assume conditions have been set up so that the mass moves in a horizontal circle. Let θ\theta be the constant angle the rod makes with the vertical. Find the frequency, Ω\Omega, of this circular motion in three different ways. ((a)) Use F=ma\mathbf{F} = m\mathbf{a}. This method works only if you have a point mass. With an extended object, you have to use one of the following methods involving torque. ((b)) Use τ=dL/dt\boldsymbol{\tau} = d\mathbf{L}/dt with the pendulum pivot as the origin. ((c)) Use τ=dL/dt\boldsymbol{\tau} = d\mathbf{L}/dt with the mass as the origin.

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