Tuesday, November 24, 2009

Scalar and vector quantities

A quantity is a characteristics of a body that can be measured with an instrument. Examples are length, area, temperature and so on.

All these quantities can be divided into two types: Scalar and Vector quantities. Normally it is quite easy to deduce whether a quantity is a scalar or a vector quantity but of you have any difficulties a list will be given later on.

Let us see how to identify a vector and a scalar quantities.

 

Scalar quantities

A scalar quantity is one that has a magnitude and a unit.

Remember the magnitude of a quantity is a number that represent its size.

Examples of scalar quantities are length, mass, temperature, etc

length = 19 m

mass = 4 kg

As you can see these quantities can only be represented by a magnitude and a unit.

 

Vector quantities

A vector quantity is one that has a magnitude, a unit and a unit.

Examples of vector quantity are acceleration, force, velocity, etc.

velocity = 100 km/h towards the north

Displacement = 100 m eastward

Force = 10 N 300 to the horizontal

As you can see all quantities that can be represented using an arrow and in which a direction make sense is a vector quantity.

For example a mass will not make sense with a direction hence it is a scalar quantity. A force make sense with a direction hence it is a vector quantity.

How to know whether a quantity is a vector or a scalar quantity

  • In case you do not know that a quantity is a scalar or a vector then you can consult this list[under construction]

 

  • Two quantities can be added or subtracted from each other unless they are both scalar or vector quantities. And the answer is a scalar
Hence if  A = B –C

and C is a scalar quantity then B must be a scalar quantity and as a result A must be a scalar quantity. The same reasoning would have applied if addition was performed.

  • If two quantities A and B are multiplied to get quantity C as in C = A*B then the nature of the quantity C would vary according to the table below.

 

    A B C Example
    Scalar Scalar Scalar Mass = density *volume
    Scalar Vector Vector Velocity = time *acceleration
    vector Vector    

 

  • If a quantity A is divided by another quantity B to obtain quantity C as in C = A/B then then the nature of quantity C would vary according to the table below.

A

 B C Example
Scalar Scalar Scalar Density = mass/volume
Vector scalar Vector Acceleration = Velocity /time
Scalar vector    
Vector Vector scalar time = velocity /acceleration
 
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5 comments:

  1. AnonymousApril 14, 2011 at 3:54 AM

    is ACCELERATION VECTOR OR SCALAR

    ReplyDelete
  2. John TanApril 14, 2011 at 9:16 AM

    Indeed acceleration is a vector quantity,

    The reason why acceleration is a vector quantity is that an acceleration is created by a force. A force is a vector quantity in that a force must act in a particular direction and it must have a direction.

    Since the force will cause acceleration in a particular direction it will act in the same direction as the force and as a result it will be a vector quantity.

    ReplyDelete
  3. AnonymousJuly 12, 2013 at 10:22 AM

    This is among the best I ever got.

    ReplyDelete
  4. AnonymousDecember 23, 2013 at 12:23 PM

    Thank you very much for this very informative article.
    Pls from what u wrote can we say generally that:
    scalar*scalar=scalar
    scalar*vector=vector
    vector*vector=vector
    whether * represents multiplication,addition, subtraction or division.
    Thank u!

    ReplyDelete
  5. John TanDecember 23, 2013 at 9:28 PM

    Note that for multiplication of two vector quantity it is slightly more difficult. I will come back to it in a later post

    ReplyDelete