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Additional info for A Guide to Physics Problems. part 12 Mechanics, Relativity, and Electrodynamics

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Consider the collision to be central and elastic and essentially instantaneous. 14 PROBLEMS a) Find the minimum value of the mass M for the incident ball to strike the system of two balls again. b) How much time will elapse between the two collisions? 24) and the azimuthal angle to describe the location of the particle (which is to be treated as a point particle). a) b) c) d) e) Write the Lagrangian for the motion. Determine formulas for the generalized momenta and Write the Hamiltonian for the motion.

B) Show that the orbit is stable with respect to small changes in the radius, and find the frequency of small oscillations. 27 Falling Chimney (Boston, Chicago) A tall, slender, cylindrical brick chimney of height L is slightly perturbed from its vertical equilibrium position so that it topples over, rotating rigidly around its base B until it breaks at a point P. Show that the most likely value for the distance of P from B is L/3. 27). 28 Sliding Ladder (Princeton, Rutgers, Boston) A ladder of mass and length stands against a frictionless wall with its feet on a frictionless floor.

39). Ignore gravity. Show that the torque must be applied to keep the axis of rotation fixed. 40 Bug on Globe (Boston) A toy globe rotates freely without friction with an initial angular velocity A bug starting at one pole N travels to the other pole S along a meridian with constant velocity The axis of rotation of the globe is held fixed. 40). 41 Rolling Coin (Princeton, Stony Brook) A coin idealized as a uniform disk of radius with negligible thickness and mass rolls in a circle. The center of mass of the coin C moves in a circle of radius and the axis of the coin is tilted at an angle with respect to the vertical.