## Momentum and Impulse

Momentum is an objects moving inertia when a mass is in motion. Learn more about momentum and impulse see examples and take a practice quiz.

Momentum (p) is the moving inertia in an object. Momentum is calculated by an objects mass times its velocity.

**p = mv**

**Momentum and Impulse Variables**

Name |
Variable |
MKS Unit |
Unit Abbreviation |

Momentum |
p | kilograms times meters per second | kg∙m/s |

Mass |
m | kilogram | kg |

Velocity |
v | meters per second | m/s |

Impulse |
J | Newtons times seconds | N∙s |

Time |
t | seconds | s |

### Momentum is Directly Related to Mass

The **larger the mass** moving the same speed the **larger the momentum**.

The 5 kg car going 10 m/s:

- p=mv
- p=(5)(10) = 50 kg∙m/s of momentum

The 35 kg car going 10 m/s:

- p=mv
- p=(35)(10) = 350 kg∙m/s of momentum

35 kg is seven times 5 kilograms and it also has seven times the momentum. The **rule of ones** could be used to determine this as well.

### Momentum is Directly Related to Velocity

If you have no velocity you have no momentum. The **larger the velocity** of the same mass the **larger the momentum**.

The 15 kg car going 0 m/s:

- p=mv
- p=(15)(0) = 0 kg∙m/s of momentum

The 15 kg car going 10 m/s:

- p=mv
- p=(15)(10) = 150 kg∙m/s of momentum

The 15 kg car going 20 m/s:

- p=mv
- p=(15)(20) = 300 kg∙m/s of momentum

The same car going double the speed has double the momentum.

**Example Problems**

**1. How much momentum does a 1575 kg Lamborghini Aventador at it's top speed of 97 m/s?**

**2. How much more momentum does an object have when it's velocity is tripled?**

### Change in Momentum and Impulse

An object changes its momentum when its velocity changes. See variations below.

### Δp = mΔv

### Δp = m(v_{f} – v_{i})

A change in momentum is created by an impulse. When a force is applied for a time period. A bat is used to change a baseballs momentum after pitched.

Impulse (J) is equal to an objects change in momentum. See the following variations of the impulse and impulse to change momentum formula below.

### J = Ft

### J = Δp

### J = mΔv

### Ft = mΔv

Since impulse equals change in momentum the unit can be the standard impulse unit (N∙s) unit or momentum's (kg∙m/s). Both units can be broken down to the same derived unit since a Newton is a (kg∙m/s^{2}).

**Example Problems**

**3. What is the change in momentum of a 0.145 kg baseball traveling 44 m/s forward when hit back at 60 m/s?**

**4. How much different is force when padding increases the time of impulse by three times?**

**5. How much force is required to stop a 0.145 kg baseball traveling at 44 m/s in 0.020 seconds?**

**Cushioning Increases Time Decreasing Force**

A car designed to crush safely on impact keeps passengers safe. Therefore, you need to replace the car but the passengers stay safe. Both cars in this animation start at 15 m/s and end at zero. Both cars with the same mass and same change of velocity have the same change in momentum.

Since impulse equals the change in momentum both cars also have the same impulse.

**Crushing Acts Like A Pillow**

Impulse is composed of force and time. A car can't change the impulse or change in momentum but crushing is like padding. Padding increases the time a force is applied and therefore decreases the amount of force. This decrease of force can lessens the impact on passengers.

**Links**

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**Collisions and Conservation of Momentum** - Back to the Main
**Impulse and Momentum and Conservation of Momentum Page** - Back to the
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