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Mechanical Momentum in Physics

Important Formula

Formula: Mechanical Momentum

$$p ~=~ \class{brown}{m} \, \class{blue}{v}$$ $$p ~=~ \class{brown}{m} \, \class{blue}{v}$$ $$\class{blue}{v} = \frac{p}{\class{brown}{m}}$$ $$\class{brown}{m} = \frac{p}{\class{blue}{v}}$$

Rearrange formula

What do the formula symbols mean?

Momentum

$$ \boldsymbol{p} $$ Unit $$ \frac{\mathrm{kg}}{\mathrm{m} \, \mathrm{s}} $$

Mechanical momentum of a body, e.g. a spaceship, a planet, a car, a particle, etc. The momentum is the product of mass $m$ and velocity $v$ of the body.

Velocity

$$ \class{blue}{\boldsymbol v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Velocity of the body. The faster the body moves, the greater the momentum $p$.

Mass

$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$

Mass of the considered body. The greater the mass, the greater the momentum $p$.

In physics, mechanical momentum is denoted by a small $ p $. To find out the momentum of a car, an ant, or even of yourself, you need to know two other physical quantities:

Mass of the body - you can measure it, for example, with the help of a weighing scale. The mass is abbreviated with $ m $ and has the unit $ \mathrm{kg} $ (kilogram).
Speed of the body - you can find it for example with a speedometer or by measuring the covered distance $ s $ and the required time $ t $. If you then divide the distance by the time, you get the speed of the body:

$$ \begin{align} v ~=~ \frac{s}{t} \end{align} $$

The velocity is abbreviated with $ v $. Its unit is $ \frac{\mathrm m}{\mathrm s} $ ("meters per second"). Why? Well, because the distance $ s $ has the unit $ \mathrm m $ and the time $ t $ has the unit $ \mathrm s $!

The spaceship has a mass and flies with a certain speed - therefore it also has a momentum!

Once you have determined the mass $ \class{brown}{m} $ of the body and its velocity $ \class{blue}{v} $, you can also easily determine the momentum $ p $ of this body. To do this, multiply the mass by the velocity:

$$ \begin{align} p ~=~ \class{brown}{m} \, \class{blue}{v} \end{align} $$

What is the unit of the momentum? You know that the mass $ m $ has the unit $ \mathrm{kg} $ and the velocity $ v $ has the unit $ \frac{\mathrm m}{\mathrm s} $. Since the two quantities are multiplied together, the result of the multiplication (i.e. the momentum) must have the unit $ \mathrm{kg} \, \frac{\mathrm m}{\mathrm s} $!

From the equation 2 for the momentum you can read two important facts:

The greater the mass of the body, the greater its momentum!
The greater the velocity of the body, the greater its momentum!

Example: Momentum of an apple

You weighed an apple and wrote down its mass $ m = 0.2 \, \mathrm{kg} $. Then you threw the apple as straight as possible and measured how far the apple flew (distance $ s $) and how long the flight took (time $t$). From this you calculated the velocity $ v ~=~ 5 \, \frac{\mathrm m}{\mathrm s} $ using the equation 1. With the equation 2 you have then determined the momentum of the apple during its flight:

$$ \begin{align} p ~&=~ m \, v \\
~&=~ 0.2 \, \mathrm{kg} ~*~ 5 \, \frac{\mathrm m}{\mathrm s} \\
~&=~ 1 \, \mathrm{kg} \, \frac{\mathrm m}{\mathrm s} \end{align} $$

Why is it important to know the momentum?
You can use momentum to calculate other physical quantities, such as kinetic energy. Also, you need the momentum in experiments with collisions, for example, when two cars collide! Also, momentum is useful if you want to compare the "impact" of different bodies to find out which body would do the most damage if it slammed into something.