Unit 4: Systems of Particles and Linear Momentum

Linear Momentum

A vector quantity that describes the 'quantity of motion' an object possesses, defined as ( \vec{p} = m\vec{v} ).

Impulse

A vector quantity that quantifies the change in momentum when a force acts on an object over time, defined as ( \vec{J} = \vec{F}_{avg} \Delta t ).

Impulse-Momentum Theorem

States that the impulse exerted on an object is equal to the change in momentum of that object: ( \vec{J} = \Delta \vec{p} ).

Closed System

A system where no mass enters or leaves.

Isolated System

A system where no net external forces act on it.

Conservation of Linear Momentum

In an isolated system, the total linear momentum remains constant over time: ( \sum \vec{p}{initial} = \sum \vec{p}{final} ).

Average Force

The total force exerted divided by the time duration over which it is applied, can be found by rearranging the impulse equation.

Elastic Collision

A collision where both momentum and kinetic energy are conserved; objects bounce off each other without any loss of energy.

Inelastic Collision

A collision where momentum is conserved, but kinetic energy is not conserved; objects may deform or generate heat.

Perfectly Inelastic Collision

A collision where two objects stick together after impact, conserving momentum but not kinetic energy.

External Force

A force that acts on an object from outside the system being considered.

Vector Quantity

A quantity having both magnitude and direction, such as momentum and force.

Impulse Approximation

An analysis used during collisions where internal forces during the impact are significantly larger than external forces.

Newton's Second Law

Originally formulated in terms of momentum: ( \vec{F}_{net} = \frac{d\vec{p}}{dt} ).

Mass (m)

A scalar quantity that represents the amount of matter in an object, measured in kilograms (kg).

Velocity ((\vec{v}))

A vector quantity that describes the speed and direction of an object, measured in meters per second (m/s).

Change in Momentum ((\Delta p))

The difference between the final momentum and initial momentum of an object: (\Delta \vec{p} = m\vec{v}f - m\vec{v}i).

Change in Velocity ((\Delta v))

The difference between final and initial velocity of an object, significant in calculating impulse.

Force ((\vec{F}))

An interaction that changes the motion of an object, defined as a vector quantity in Newtons (N).

Kinetic Energy

The energy of an object due to its motion, dependent on its mass and velocity.

Acceleration ((\vec{a}))

The rate of change of velocity of an object, described as a vector quantity measured in meters per second squared (m/s²).

Momentum Vector ((\vec{p}))

The vector quantity representing the momentum of an object, defined by (\vec{p} = m\vec{v}).

Force vs. Time Graph

A graph representing the relationship between applied force and time, used to calculate impulse as the area under the curve.

Collision

An interaction between two bodies that results in a transfer of momentum.

Net External Force

The total force acting on a system from outside that can change its momentum.

Worked Example

A problem-solving approach often used to illustrate how to apply theory to practical situations.

Safety Engineering

The field focused on preventing accidents through the design of systems and structures, including the application of impulse concepts to airbags.