In Physics,
we have to deal with lots of physical quantities. All the measurable quantities
are known as physical quantities. Some examples of the physical quantities are
length, mass, velocity, weight and acceleration etc. While teaching physical
quantities, when we tell the students that all the measurable quantities are known
as physical quantities, some students frequently ask the question that which
quantities are not measurable. I try to provide an answer to this question with
the help of examples. The quantities like love, honesty and kindness are not measurable,
therefore, we can’t say them physical quantities. For example, if you love
someone, you just express your love in words rather than in kilograms, kilometres
or miles. Let’s move towards the basic topic. These physical quantities are
divided into two types. These two types of physical quantities are known as
scalars and vectors. When we have to deal with lots of physical quantities, it
is difficult for us to differentiate scalars from vectors. The difference
between scalars and vectors is given below;

#
What are Scalars?

A physical quantity
which is fully described just with the help of magnitude is known as a scalar.
It means that to describe the scalar quantity, we just require a number. Some
essential examples of the scalars are speed, mass, temperature and time etc.

Ø If you go to a shop to buy sugar, you
can easily buy the sugar just by telling the magnitude of the sugar. For example,
if you want to buy one kg sugar, you just need to tell that you need one kg of
sugar and you don’t need to tell the direction. It means that you don’t need to
tell the shopkeeper that you require one kg of sugar in the East, West or North.

#
Some Essential Points of Remember about Scalar Quantities

If we want
to understand scalar quantities effectively, we should also try to remember these
essential points;

Ø The scalar quantities only have
magnitudes and these quantities don’t have directions.

Ø If you are changing the scalar
quantity, it means that you are changing the magnitude of the scalar quantity.

Ø These are one dimensional.

Ø To add and subtract the scalar quantities,
you will have to follow the basic rules of the algebra.

Ø We can’t resolve the scalar
quantities. It means that scalar quantities have the same values in all the
directions.

#
What are Vectors?

A physical
quantity which is completely described with the help of magnitude, as well as
direction, is known as a vector quantity. It means that to completely describe
a vector quantity, you will have to tell magnitude as well as direction. Some essential
examples of the vector quantities are velocity, acceleration and force etc.

Ø If you want to accelerate a vehicle,
you will have to ask someone to apply force on it. When you are asking him to
apply force on the vehicle, you will have to tell him to apply force either in
the backward direction or in the forward direction.

#
Some Essential Points of Remember about Vector Quantities

If we want
to effectively understand the vector quantities, we should try to remember these
essential points;

Ø All the vector quantities are
comprised of magnitude and direction. Therefore, you can easily describe the vector
quantities with the help of magnitude as well as direction.

Ø If you are changing the vector
quantity, it means that you are changing the magnitude as well as the direction
of the vector quantity.

Ø These quantities have up to three
dimensions.

Ø To add two or more vectors, you will
have to use head-to-tail rule.

#
Key Differences Between Scalar and Vector Quantities

To differentiate
between scalars and vectors, you will have to understand these key differences.

##
Ø
Description

The first
main difference between scalar and vector quantities is that they are described
in two different ways. First, if you want to describe the scalar quantities,
you will have to provide magnitudes only and you don’t need to provide the
direction. On the other hand, if you want to describe the vector quantities,
you will have to provide magnitude as well as direction.

##
Ø
Dimensional

The scalar
quantities are always one dimensional. On the other hand, vector quantities can
be one, two or three dimensional.

##
Ø
Division

We can
divide a scalar quantity with the help of another scalar quantity. On the
other, we can’t divide a vector quantity with another vector quantity.

##
Ø
Direction

We can’t resolve
the scalar quantities. Its reason is that a scalar quantity has the same value
in all the directions. On the other hand, we can easily resolve a vector
quantity in the mutually perpendicular directions with the help of the adjacent
angles.

##
Ø
Relationship Between Scalars and Vectors

When we
perform any mathematical operation between a scalar quantity and a vector
quantity, its result is always in the form of a vector quantity.

##
Ø
Mathematical Rules

To perform different
mathematical operations between two or more than two scalar quantities, we have
to follow ordinary rules of algebra like subtraction, addition and multiplication
etc. On the other hand, to perform different mathematical operations between
two or more than two vector quantities, you will have to follow vector algebra rules.

##
Ø
Change

While using
scalars and vectors in Physics, sometimes, we have to change them. If we are
changing the scalar quantity, it means that you are changing the magnitude of
the scalar quantity. On the other hand, if you are changing a vector quantity,
you are not only changing the magnitude of the vector quantity but you are also
changing the direction of the vector quantity.

##
Ø
Representation

If we want
to represent a scalar quantity, we can easily represent it with the help of its
symbol. Some examples are m and s etc. On the other hand, if we want to
represent a vector quantity, we will have to use the symbol as well as an arrow
which has two parts head and tail.

##
Ø
Examples

Scalars and
vectors are two different quantities. Therefore, these two quantities also have
different examples. Some examples of scalars are mass, length and time etc. On
the other hand, some examples of the vectors are acceleration, force and velocity
etc.

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Posts:

#
Differentiate Scalars from Vectors in the Given Set of Physical Quantities

After understanding
the key differences between scalars and vectors, you can easily differentiate
the scalars from vectors in the given set of physical quantities. Differentiate
the scalars from the vectors in the following set of the physical quantities;

Length, velocity, accelerations, mass, temperature
and force.

You can
easily differentiate scalars and vectors just by knowing that which quantities
are completely described with the help of help magnitude only and which
quantities require magnitude as well as direction for their complete
description.

Scalar Quantities

Ø Length

Ø Temperature

Ø Mass

Vector
Quantities

Ø Velocity

Ø Force

Ø Acceleration

#
Similarities Between Scalars and Vectors

Along with
understanding the key differences between these two quantities, you should also
know that there are also some similarities between these two quantities. These
similarities are given below;

Ø While describing the differences
between these two quantities, we have not discussed the unit. Its reason is
that both scalars and vectors require a unit for their complete description.
Therefore, it is a similarity between these two quantities and it is not a
difference.

Ø As scalars are vectors are two kinds
of physical quantities. Therefore, both scalars and vectors are measurable
quantities.

Ø Another similarity between these two quantities
is that we require dimension to completely describe these two quantities.

Ø Either we are discussing the scalar
quantities or the vector quantities we are discussing the physical quantities.

#
Conclusion

After a brief
explanation about the scalars and vectors, we can conclude our discussion in a few
points. The main difference between scalars and vectors is in their direction
because to describe the scalar quantity, we don’t require direction and to
describe the vector quantity, we require direction. For example, if we are
discussing the scalars, it means that we are discussing the amount of the
object. On the other hand, if we are discussing vectors, it means that we are
discussing its amount as well as direction.

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