Mammoth Memory

Vectors and scalars

Scalar

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

The figure you get from bathroom scales is a scalar as it only gives you a number (magnitude) and no direction

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.

A convector being driven noth at 70mph has magnitude (70mph) and direction (north) and so is a vector

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

The arrow representing john walking north 20 metres is a vector as it has a magnitude (20 metres) and a direction (north)

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.

The displacement of the person from the tree is equal to the trees displacement position from you, minus the persons displacement position from you

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

Adding vector a (blue vector) to vector b (red vector) the resultant green vector will be the same as adding vector b (red vector) to vector a (blue vector)

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

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

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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