A projectile of mass m moves to the right with a speed vi (see figure below). The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision. The moment of inertia of a rod is I = Md² and the moment of inertia of a particle is I = mr². 12 a. What is w, the angular speed of the system after the collision. Answer: W= mdvi Md²+1md² 12 energy before the collision? Answer: KE¡ = 1½ m(v;)². b. What is the kinetic C. What is the kinetic energy after the collision?

A block of mass m = 0.75 kg, moving at constant speed v = 4.00 m/s, slides along a horizontal, frictionless surface and collides with and sticks to the end of an initially vertical, stationary thin rod, of mass M = 5.50 kg, and length L = 0.750 m. See the figure below. The other end of the rod is attached to a horizontal frictionless pivot which allows the mass-rod system to rotate to an angle θ with the vertical direction. What is the maximum angle θmax the rod makes with the vertical? (The moment of inertia of a uniform thin rod about an axis through one end is given by ML2/3)

One end of a massless rigid rod of length is attached to a wooden block of mass M resting on a frictionless, horizontal tabletop, and the other end is attached to the table through a pivot (see figure below). A bullet of mass m traveling with a speed v in a direction perpendicular to the rod and parallel to the table impacts the block and embeds itself inside. (a) What is the angular momentum of this system around a vertical axis through the pivot after the collision? (Use any variable or symbol stated above as necessary. Enter your answer as an expression for magnitude.) L = M (b) What is the fraction of the bullet's initial kinetic energy that is lost to internal energy during the collision? (Use any variable or symbol stated above as necessary. Enter your answer as an expression for magnitude.) AK K;

A projectile of mass .050 kg moves to the right with a speed of 4.0 m/s. The projectile strikes and sticks to the end of a rod of mass 0.8 kg, at length 1.2 m from the rod's centre. The rod may rotate freely around a stationary axle pinned through the rod's centre of mass. Find the magnitude of the angular velocity, ω, of the system right after the collision.