LINEAR MOMENTUM The rate of change of the linear momentum of a particle is equal to the net force acting on the particle.

Total momentum

Change in momentum

Conservation of Linear Momentum Total momentum of two-ball system is conserved momentum before = momentum after

Collisions and Impulse Before During (strong forces on each other for a short time) After

Elastic Collisions (kinetic energy is conserved) Collisions Inelastic Collisions (kinetic energy is not conserved) Linear momentum is conserved in both cases

Inelastic Collisions in 1-Dimension Completely Inelastic Collision

Ballistic Pendulum The ballistic pendulum is a device to measure the speed of a projectile such as a bullet. The projectile of mass m is fired to a large block of mass M, which is suspended like a pendulum. As a result of the collision, the pendulum and projectile swing up to a maximum height h. Determine the relationship between the initial speed of the projectile v and the maximum height h.

Elastic Collisions in 1-Dimension Linear momentum is conserved Kinetic Energy is conserved

Unequal masses, target at rest

Collisions in Two Dimensions Before During After

Two billiard balls of equal mass move at right angles and meet at the origin. Assume the collision is elastic, what is the final direction of the A ball and what are the balls’ final speeds?

CENTER OF MASS (CM) The center of mass of a body or a system of bodies is the point that moves as if all of the mass concentrated at that point and all forces acting on it.

Solid Bodies Objects with uniform density