1. Show that the moment of inertia in the figure is . M is the total mass.
  1. Show that the moment of inertia in the figure is .M is the total mass.
  1. Show that the moment of inertia in the figure is .M is the total mass.
  1. A solid cylinder of mass M and radius R unwinds on a vertical string. (a) Use the energy method to show the speed of the cylinder after it falls a distance h starting from rest is . (b) Use the result of (a) to find the accerlation of the CM. (c) From the total forces and torques on the cynlinder, find the the accerlation of the CM.. (d) What is the tension? (e) What is the tension needed to make the cylinder spin but not fall? What is the angular acceleration in this case?(ICM=)
  1. A ladder of Length L and weight W rests on a rough floor and against a frictionless wall. The coefficient of static friction at the floor is s=0.6. (a) Find the maximun angle  to the wall such that the ladder does not slip, (b) the force exerted by the wall at this .
  1. A solid sphere of radius R has a density that varies as , where r is the distance from the center. Determine that variation of the field strength with r within the sphere (r<R).
  1. A particle of mass m=0.5 kg moving at speed u=4 m/s strikes a dumbell consisting of two blocks of mass M=1 kg seperated by a massless rod of length 2 m. The dumbbell and the particle are free to slide on a horizontal surface. Find: (a) the speed of the center of mass of the system after the particel sticks to one block; (b) the angular velocity of the the system about the center of mass.
  1. A pendulum consists of a uniform rod of mass 1.2 kg and length 60 cm. At its end is a disk of radius 5 cm and mass 0.4 kg. It is released when the rod is 30o to the vertical. (a) What is the moment of inertia about the axis at the top of the rod? (b) What is the speed of the lowest point when the rod is vertical. (ICM of rod=, ICM of disk=).
  1. Find the field strength at the center of a thin uniform semicircular ring of radius R and mass M.
  1. A particle of mass m moving in s circle and the centripetal force is provided by the rope. The initial angulat momentum is L0. The force is changed in such a way that the radius of the motion decreases from r1 to r2. (a) How does the force vary as a function of r? (b) Calculate the work done by the force. (c) What is the kinetic energy of the particle? (d) Does the work-energy theorem apply?