Athin, uniform, metal bar, 3.00 m long and weighing 90.0 n , is hanging vertically from the ceiling by a frictionless pivot. suddenly it is struck 1.60 m below the ceiling by a small 3.00-kg ball, initially traveling horizontally at 10.0 m/s . the ball rebounds in the opposite direction with a speed of 5.00 m/s. find the angular speed of the bar just after the collision? why linear momentum not conserved?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.