PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics
Action and Symmetry, Ch Multipliers, non-holonomic constraints and forces outside the potential
Problem
A coin of radius a=1.0cm starts upright on a table at (x,y,θ,ψ)=(0,0,0∘,0), where θ is its heading and ψ its spin angle about its own axle. Using only pivots (turning the heading on the spot, ψ unchanged) and straight rolls (heading fixed, no slipping), describe a path that carries the coin to the point (x,y)=(0.30m,0.40m) with its final heading equal to its initial heading, θ=0∘.
((a)) State the sequence of pivots and rolls, giving the angle of each pivot and the distance of the roll.
((b)) Give the coin's spin angle ψ (in radians, taking rolling forward as increasing ψ) on arrival.