A solid disc ( I = mr 2 ) has a radius of 10 cm and a mass of 2 kg rotated on its axis with an angular velocity of 20 rad/s in a horizontal position. Another disc which has the same radius but a mass of 1 kg is dropped by exactly one axis with the first disc so that it rotates together. Define: a. first disc angular momentum ! b. system final angular velocity

#3. Suppose a large hollow sphere made from a ream (500 8.5 × 11 inch sheets) of paper has a mass of 2.27 kg and a radius of 1.55 meters if the sheets are combined in such a way that no area of the sphere is left uncovered and none of the constituent sheets overlap. What is the moment of inertia of the sphere? A. 1.91 kg·m^2 #4. Suppose the paper sphere in #3 is made to rate exactly once per second. What is the angular speed ω of the sphere? A. 1.00 Rad/s B. 3.14 Rad/s C. 6.28 Rad/s D. 12.6 Rad/s In #4, what is the kinetic energy of the paper sphere which rotates exactly once per second? A. 42.0 J B. 71.6 J C.102J D.136J

m2 m1 Consider the light, rigid rod shown in the figure above. Its length is 1.9 m. Attached to the ends of the rod are two masses with masses m1 = 3.8 kg and m2 = 3.3 kg. The combination rotates in the xy plane about a pivot through the center of the fod. Determine the angular momentum of the system about the centre when the speed of each particle is 4.0 m/s.

3. The figure to the right shows a rod that is connected to a frictionless table through a pin-labeled by A -placed through the center of it. (You are looking down on the table.) The rod has mass m and length l. Although the rod is initially at rest, it can rotate freely (without friction) about the pin. A small particle with mass m/3, and moving with an initial velocity vo vo collides with the end of the rod. After the collision the mass stops moving, and the rod starts rotating with angular velocity w. I would strongly recommend that you draw a free body diagram for the rod in parts a and b. a. Linear momentum is not conserved for this collision. Explain in detail why. b. Angular momentum is conserved about the pivot. Explain in detail why. c. What is w? Express it in terms of vo, and l. d. Is energy conserved in the collision? Justify your answer by calculating the change in energy of the system in the collision. e. After a time T after the collision the rod will rotate around and…

8. The image below depicts a street light standard that has been blown off of vertical by high winds during storm. A force of 1000N is being applied to the standard in order to "upright" the standard. Determine the magnitude and sense of the Moment about point A at the instant depicted. N-m. Be sure to include whether the Moment is Moment = Positive or Negative for this 2D problem. B 6 m 75° 3 m

250 m/s 140 m/s Pivot A uniform stick 1.0 m long with a total mass of 250g pivoted at its center. A 8.0-g bullet is shot through the stick midway between the pivot and one end. The bullet approaches 250 m/s and leaves at 145 m/s. With what angular speed is the stick spinning after the collision?

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17. A bullet traveling with an initial speed vo enters an door imbedding Hinge itself from the side opposite the hinges, as shown in the overhead view of the figure. Ignoring air resistance and the friction due to the hingers, which of the following statements must be true? a. The angular momentum of the system consisting of the -18.0 kg door and the bullet is conserved. b. The linear momentum of the system consisting of the door and the bullet is conserved. 0.005 kg c. The total mechanical energy of the system consisting of the door and the bullet is conserved. d. The total kinetic energy of the system consisting of the door and the bullet is conserved.

2. A weightless rod of length 2L carries two equal masses m at its ends and forms angle 8 with the vertical z axis. The rod rotates with angular velocity w about the z axis. A) Find the Lz component and the Lz vector of the angular momentum of the system. B) It is logical that the vector LZ is not the angular momentum of the system parallel to the z-axis? For what angle 8 is L parallel to z axis?