A particle of mass moves in an unspecified central potential about a fixed centre

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics

Action and Symmetry, Ch Symmetry, Noether's theorem and what is conserved

Problem

A particle of mass

m=0.25\ \mathrm{kg}

moves in an unspecified central potential about a fixed centre, subject also to a linear drag force

-b\mathbf v

with

b=0.040\ \mathrm{kg\,s^{-1}}

, represented by the Rayleigh dissipation function

\mathcal F=\tfrac12 b(\dot r^2+r^2\dot\theta^2)

. At

t=0

its angular momentum about the centre is

p_\theta(0)=0.60\ \mathrm{kg\,m^2\,s^{-1}}

. Find

p_\theta

t=8.0\ \mathrm{s}