Scalar vs Vector

Even a person without a background in physics has a collection of words that can be used to describe moving objects.

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Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a sufficient vocabulary for describing the motion of objects.

In physics, we use these words and many more.

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We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration.

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As we will soon see, these words are associated with mathematical quantities that have strict definitions.

The mathematical quantities that are used to describe the motion of objects can be divided into two categories which can be distinguished from one another by their distinct definitions:

• Scalars are quantities that are fully described by a magnitude* alone.

• Vectors are quantities that are fully described by both a magnitude and a direction.

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*Magnitude only refers to the amount of something. If you have trouble remembering that, skip over the word and read the sentence again - it still makes sense!!

Distance

Mass

Time​​

Density

Volume

Energy​

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• The tail is the starting position.

• The head is the ending position.

• The magnitude represents how long or large the vector is.

  • For example, a vector representing 100 should be twice as long as a vector representing 50. ​

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​How To Draw a Vector

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Displacement

Velocity

Momentum​

Force

Acceleration

Magnetic Field​

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