Linear Momentum Center of Mass Introduction q Collisions

Introduction q Collisions q Impulse n n and Linear Momentum Single Collision Series of

Center of Mass for a System of Particles The center of mass of a

Center of Mass for a Solid Body Differential mass element dm Uniform density

Newton’s 2 nd Law for a System of Particles System of particles A firework

Linear Momentum Particle System Conservation of Linear Momentum If no net external force acts

Impulse and Linear Momentum Definition of Impulse Collision of two particle-like bodies Impulse–Linear Momentum

Momentum and Kinetic Energy q Closed system (no mass enters or leaves) q Isolated

Inelastic Collisions in 1 D Conservation of Linear Momentum Completely Inelastic Collision Velocity of

Elastic Collisions in 1 D In an elastic collision, the kinetic energy of each

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Linear Momentum & Center of Mass

Introduction q Collisions q Impulse n n and Linear Momentum Single Collision Series of Collisions q Momentum and Kinetic Energy q Inelastic Collisions in One Dimension n n One-Dimensional Collision Completely Inelastic Collision q Elastic Collisions in One Dimension q Collisions in Two Dimensions

Center of Mass for a System of Particles The center of mass of a body or a system of bodies moves as though all of the mass were concentrated there and all external forces were applied there. 2 bodies, 1 dimension n bodies, 3 dimensions, vector equation

Center of Mass for a Solid Body Differential mass element dm Uniform density

Newton’s 2 nd Law for a System of Particles System of particles A firework rocket explodes A grand jeté

Linear Momentum Particle System Conservation of Linear Momentum If no net external force acts on a system of particles, the total linear momentum P of the system cannot change. If the component of the net external force on a closed system is zero along an axis, then the component of the linear momentum along that axis cannot change.

Impulse and Linear Momentum Definition of Impulse Collision of two particle-like bodies Impulse–Linear Momentum Theorem Steady stream of projectiles

Momentum and Kinetic Energy q Closed system (no mass enters or leaves) q Isolated system (no external net force) q Elastic collision (kinetic energy conserved) q Inelastic collision (kinetic energy not conserved) q Completely inelastic collision (bodies always stick together) In a closed, isolated system containing a collision, the linear momentum of each colliding body may change but the total momentum of the system cannot change, whether the collision is elastic or inelastic.

Inelastic Collisions in 1 D Conservation of Linear Momentum Completely Inelastic Collision Velocity of Center of Mass

Elastic Collisions in 1 D In an elastic collision, the kinetic energy of each colliding body may change, but the total kinetic energy of the system does not change. Stationary Target Moving Target