Figure I: Before
Figure II: After
1981M3. A thin, uniform rod of mass M1 and length L , is initially at rest on a frictionless horizontal surface. The moment of inertia of the rod about its center of mass is M1L2/12. As shown in Figure I, the rod is struck at point P by a mass m2 whose initial velocity v is perpendicular to the rod. After the collision, mass m2 has velocity
−21v as shown in Figure II. Answer the following in terms of the symbols given.
a. Using the principle of conservation of linear momentum, determine the velocity v′ of the center of mass of this rod after the collision.
b. Using the principle of conservation of angular momentum, determine the angular velocity ω of the rod about its center of mass after the collision.
c. Determine the change in kinetic energy of the system resulting from the collision.