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Chapter 9, System of Particles
Center of Mass
Momentum and Conservation
Impulse
Rocket
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
n bodies, 3 dimensions, vector equation
Center of Mass for a Solid Body
Differential mass element dm
Uniform density
Newton’s 2nd Law for a System of Particles
System of particles
A grand jeté
A firework rocket explodes
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
Impulse–Linear
Momentum Theorem
Collision of two
particle-like bodies
Steady stream of
projectiles
Momentum and Kinetic Energy
Closed system (no mass enters or leaves)
Isolated system (no external net force)
Elastic collision (kinetic energy conserved)
Inelastic collision (kinetic energy not conserved)
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 P of the system cannot
change, whether the collision is elastic or inelastic.
Inelastic Collisions in 1D
Conservation of Linear Momentum
Completely Inelastic Collision
Velocity of Center of Mass
Elastic Collisions in 1D
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
Other Applications
Sample Problem 9-8, 9-10
Rocket System
Rocket equations