Mammoth Memory

Vectors and scalars

Scalar

 Scalar – Quantity having only magnitude (not direction). It’s only a number.

The scales (scalar) only give you a number.

 

Scalar quantities include:

  • Speed
  • Area
  • Value
  • Temperature
  • Distance
  • Time
  • Mass

To name but a few.

All these examples only have size (magnitude). Unlike a vector, it doesn’t mention direction. 

 

Scalars are easy to use just add the numbers

 

Example 1

3m2

+

4m2

=

7m2

Area

+

Area

=

Area

 

Example 2

A person buys a bag of sugar labelled with a mass of 500g. The mass of this bag of sugar is a scalar quantity. It only needs a number to describe it.

 

 

Vector

Vector – Is a line which has magnitude (how long it is) and direction.

they drove the con vector dfor a long period of time northwards.jpg

They drove the con vector for a long period of time (how long) northwards (and direction).

 

A vector is a physical quantity that has both a magnitude and a direction

 

Examples of vectors:

  • Velocity (speed and direction)
  • Displacement (distance in a given direction)
  • Force (you push something with strength (magnitude) in a particular direction say up a hill)
  • Acceleration (is a vector quantity because it has both magnitude and direction when an object has a positive acceleration, the acceleration occurs in the same direction as the movement of the object. When an object has a negative acceleration (its slowing down) the acceleration occurs in the opposite direction as the movement of the object).

 

 

Example 1

If a car travels at 70mph in the direction of East. We know the magnitude which is 70mph and going East is the direction. Speed and direction of the car (magnitude and a direction) together form a vector we call velocity.

 

Example 2

John walks 20 meters. The direction north together with the distance.jpg

John walks north 20 metres. The direction”north” together with the distance “20 metres” is a vector called displacement.

 

Example 3

Vectors can be added or subtracted from each other to produce a resultant vector.

If you were stood at the intersection of the x, y, z.jpg

If you were stood at the intersection of the x, y and z axis in the image above the person in the image is at a displacement from the tree. This displacement is equal to the trees displacement position from you, minus the persons displacement position from you.

 

Example 4

It does not matter which order you add vectors together the resultant vector will be the same.

If you add vector a (blue vector) to vector b (red vector) the resultant green vector will be the same as if you added vector b (red vector) to vector a (blue vector).

 

Example 5

An apple falls doen at 10 meters per second.jpg

An apple falls down at 10 metres per second. The direction “down” combined with the speed “10 metres per second” is a vector (this kind of vector is called velocity).

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