A projectile of mass m moves to the right with a speed v; (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 = moment of inertia of a particle is I = mr². Md² and the 12 a. What is w, the angular speed of the system after the collision. Answer: W= mdvi Md²+md² b. What is the kinetic energy before the collision? Answer: KE₁ = m(v₁) ². c. What is the kinetic energy after the collision? m²d² Answer: KEy = 2 ( M² +4 m²) (v₁) ² 1/ 12

A disc of radius R = 0.41 m and of mass M = 1.22 kg is rotating with the initial angular momentum ωi = 0.51 rev/s on a frictionless horizontal plane. You drop a small clay piece of mass m = 0.19 kg vertically, it lands, and is stuck on a point of the rim of the disc at the distance R = 0.41 m from the center of the disc (Fig.9). The initial moment of inertia of the disk about the axis of rotation through its center is Ii = MR2/2. What is the angular velocity of the disc-clay system in rev/s after the collision? Keep three significant figures for the answer. Note the clay piece has negligible size so that it can be treated as a point.

A rod of mass M = 3.25 kg and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 65 g, moving with speed v = 5.25 m/s, strikes the rod at angle θ = 51° from the normal at a distance D = 2/3 L, where L = 1.3 m, from the point of rotation and sticks to the rod after the collision. 1. What is the angular speed ωf of the system immediately after the collision, in radians per second?

Shown below is a small particle of mass 20 g that is moving at a speed of 10.0 m/s when it collides and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and is perpendicular to the page. The cylinder has a mass of 0.5 kg and a radius of 10 cm, and is initially at rest. (a) What is the angular velocity of the system after the collision? (b) How much kinetic energy is lost in the collision?

A thin rod with a length of 4.0 m and a mass of 4.2 kg is initially at rest. It is capable of spinning around a frictionless axle that goes through the top of the rod. A 2.5 kg mass of clay collides perfectly idealistically with the bottom of the rod. The clay was traveling perfectly horizontally with a speed of 12 m/s before the collision. How fast will the rod with the clay attached to it rotate around the axle in radians per second? The only external force on the clay/rod system come from the axle, which exerts no torque about itself.

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. Select one: a. 0.00 rad/s b. 0.27 rad/s c. 0.53 rad/s d. None of the other answers are correct e. 1.05 rad/s

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. mdvi Md²+1md² 12 b. What is the kinetic energy before the collision? Answer: KE¡ = m(v¡)². c. What is the kinetic energy after the collision? (0₁)² Answer: W= 1 m²d² Answer: KE₁ = = =+M₁2² +² md² 12 4 m O d M O 3

A physical pendulum consists of a vertical board of of mass 5.8 kg, length 172 cm, and width 5 cm hanging from a horizontal, frictionless axle. A bullet of mass 145 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?

A sphere of mass 1.0 kg and radius 0.21 m is suspended on the rod of length 0.49 m and mass 0.43 kg as it is shown in the figure. System can rotate around uppermost point. A bullet of mass 0.02 kg strikes the sphere as it shown in the figure (aiming directly to the center of the sphere) and embeds. Find minimum velocity of bullet which allows this system to just clear the top. The answer is 300.719752599215. Please show all steps on how to get to that answer.

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;