A particle of mass is constrained to move on a fixed
PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics
Action and Symmetry, Ch Constraints, generalised coordinates and Lagrange's equations twice over
Problem
A particle of mass 0.50kg is constrained to move on a fixed, frictionless circular track of radius R=0.30m lying in a vertical plane. Let θ be the angle measured from the bottom of the track. A small motor applies a constant force of magnitude F=0.80N tangent to the track, in the direction of increasing θ, in addition to gravity.
((a)) State the dimension and shape of the configuration space of this particle.
((b)) Find the generalised force Qθ due to the motor alone, and state its units.