Question

A solid, horizontal cylinder of mass 15.0 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

______rad/s

Answer 1

Solution : given: mass of a solid cylinder is m: 15.0kg and radius 92 = 1.00m initial angular speed W,- 7.50 gad's We know that moment of inentia for a solid cylinder about cylinder axis is I o mo? mass of piece is m'= 0.250 kg distance of mass of piece from the center of rotation is d= 0.900m we assume final angular speed is Wz We know that conservation law of angular momentum in II, W, = I₂ W₂ where I = 1 = mu? and I = It m'd² I, - 1 monum'de : ;, W, .: W, Ia w (mat)w, (mn²+ m² (man2+2 mid ² 15.0 x11.00x7.50 115.08.01.0012 + 2x0.250x (0.90o)?) W2 = 7.30 rad's