# Momentum

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Momentum

Momentum ( $$p$$ or $$\rho$$ (Greek symbol rho) ) (also known as linear motion or translational momentum) of an object is the amount of mass in motion.  Momentum is a vector quantity having magnitude and direction, some of these include acceleration, displacement, drag, force, lift, thrust, torque, velocity, and weight.

### Momentum Formula

$$p = m v$$          $$momentum \;=\; mass \;\;x\;\; velocity$$

Where:

$$p$$ or $$\rho$$ (Greek symbol rho)  = momentum

$$m$$ = mass

$$v$$ = velocity

## Mass Distributed Momentum

### Mass Distributed Momentum Formula

$$p = {mv}_i \; - \; {mv}_f$$          $$momentum \;=\; initial \; mass \; velocity \; - \; final \; mass \; velocity$$

Where:

$$p$$ = momentum

$${mv}_i$$ = initial mass velocity

$${mv}_f$$ = final mass velocity

## Momentum Change in Velocity

### Momentum Change in Velocity Formula

$$p = m \left( v_i \; - \; v_f \right)$$          $$momentum \;=\; mass \; \left( \; initial \; velocity \; - \; final \; velocity \; \right)$$

Where:

$$p$$ = momentum

$$m$$ = mass

$$v_i$$ = initial velocity

$$v_f$$ = final velocity

## Momentum Change in Momentum

### Momentum Change in Momentum Formula

$$p = p_i \; - \; p_f$$          $$momentum \;=\; initial \; momentum \; - \; final \; momentum$$

Where:

$$p$$ = momentum

$$p_i$$ = initial momentum

$$p_f$$ = final momentum

## Momentum Diffusion

Momentum diffusion also known as diffusion, or spread of momentum between particles (atoms or molecules) of matter, often in the liquid state. In fluids, this is caused by viscosity.

## Elastic Collision Momentum

Momentum is a conserved quantity meaning the total momentum of a system will always stay the same no matter the changes to the system.

### Elastic Collision Momentum Formula

$$p_t = p_i1 \; + \; p_i2 = p_f1 \; + \; p_f2$$          $$total \; momentum \;=\; initial \; momentum \; 1 \; + \; initial \; momentum \; 2 \;=\; final \; momentum \;1 \; + \; final \; momentum \;2$$

Where:

$$p_t$$ = total momentum

$$p_i$$ = initial momentum

$$p_f$$ = final momentum

## Rotational Momentum

Rotational momentum ( $$L$$ ) (also known as angular momentum) is how much an object is rotating.

### Rotational Momentum FORMULA

$$L = r p$$          $$rotational \; momentum \;=\; vector \; length \;\;x\;\; linear \; momentum \; vector$$

$$L = I \omega$$          $$rotational \; momentum \;=\; moment \; of \; inertia \;\;x\;\; angular \; velocity$$

Where:

$$L$$ = rotational momentum (angular momentum)

$$r$$ = vector length, directed from the center of rotation to the momentum point

$$p$$ = linear momentum vector

$$I$$ = moment of inertia

$$\omega$$ (Greek symbol omega) = angular velocity