Small spheres of radius "r" are incident with velocity v on a stationary hard sphere of radius "R" and scatter elastically. What is the total scattering cross section?
Consider a uniform disc with mass m and radius a that has a massless string wrapped around it with one end attached to a fixed support and allowed to fall with the string unwinding as it falls, as shown in the figure.
Use y and φ as the generalized coordinates to describe the system. Find the equations of motion for y and of the falling disc and the forces of constraint using the method of Lagrange multipliers.
A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R as shown in the figure. The only external force is that of gravity. If the hoop starts rolling from rest on top of the big cylinder, find, by the method of Lagrange multipliers, the point at which the hoop falls off the cylinder.
