PHI 203 Final: PHYS 203 Princeton Final2005
136 views5 pages
Document Summary
Fall 2005: (30 points) toy car toy car. There is no friction in the axles of the wheels. R: assuming that the wheels of the car roll without slipping on the floor, calculate the frequency of small oscillations of the car. Now consider the possibility that the wheels can slip on the floor: write down the lagrange equations of motion including the equation of constraint. 0: find the maximum amplitude of the car oscillation before the wheels begin to slip. The undetermined multiplier gives the force of friction. 2 mk: (30 points) rotating wire and mass. A y-shaped massless wire with two arms at 45 is free to rotate around a vertical axis. A small bead of mass m is free to slide on one arm of the wire. 45 r m: write down the hamiltonian for the system. Start with 3 degrees of freedom in cylindrical coordinates. Since r = z, can reduce it to two variables: rmh.