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Physics is a mathematical field of study. There is a mathematical foundation for the fundamental notions and principles. Throughout our physics studies, we will come across a variety of topics that have a mathematical foundation. While we will place a strong focus on the conceptual nature of physics, we will also pay close attention to its mathematical aspect.
Words can be used to describe the motion of objects. Even if you don’t have a physics background, you can come up with a list of adjectives to describe moving objects. Going quickly, stopping, slowing down, speeding up, and turning are just a few of the words and phrases that can be used to describe the motion of objects. These and other terms are used in physics. Words like distance, displacement, speed, velocity, and acceleration will be added to this vocabulary list. These terminologies are related to mathematical quantities that have strict definitions, as we will see shortly. There are two types of mathematical quantities that are used to explain the motion of objects. The value can be a vector or a scalar. The distinction between these two categories can be seen in their definitions.
1.Scalars are quantities that may be completely defined by a single magnitude (or numerical value).
2.Vectors are quantities with both a magnitude and a direction that are completely specified.
Scalar Quantity
A scalar quantity is one that is defined solely by its magnitude. Mass, Charge, Pressure, and other scalar quantities are examples.
Vector Quantity
Vector quantities have both magnitude and direction and follow the equations of vector addition. Vectors include things like displacement, velocity, and force.
Only if all three of the above conditions are met is a quantity called a vector. Current, for example, despite having both magnitude and direction, is not a vector since it does not obey vector laws of addition
Direction Of Vector
Vector a shown in digram can be represented by
a=axi+ayi+azi
aX- component of vector along x-axis
ay- component of vector along y-axis. az- component of vector along z- axis
where i,j and k are unit vector aling x ,y,z direction
Difference Between Scalar And Vector Quantity
| Vector | Scalar |
Defination | A physical Quantity with both magnitude and direction | A physical quantity with only magnitude |
Representation | A number direction using unit cap | A number and unit |
Symbol | Quantity symbol in bold and arrow sign above | Quantity Symbol |
Direction | Yes | No |
Vector Addition
Adding two or more vectors is known as vector addition. When adding vectors, we use the addition operation to combine two or more vectors to create a new vector that is equal to the total of the vectors. Vector addition is utilized in physical quantities where velocity, displacement, and acceleration are represented by vectors.
Vectors are written with an alphabet and an arrow over them (or) with an alphabet written in bold as a mix of direction and magnitude. Vector addition can be used to combine two vectors, a and b, and the resultant vector can be expressed as a + b. Before we can learn about the properties of vector addition, we must first understand the requirements that must be met while adding vectors. The following are the requirements:
Only vectors of the same type can be combined together. Acceleration, for example, should be added with only acceleration and not mass.
We can’t combine vectors with scalars.
Consider the following two vectors: C and D.
C= Cxi + Cyj + Czk
D = Dxi + Dyj + Dzk
C + D = (Cx + Dx)i + (Cy + Dy)j + (Cz+ Dz ) k is the resultant vector (or vector sum).
Conclusion
In conclusion, a two-dimensional vector has two components, i.e., an impact in two different directions. Methods of vector resolution can be used to determine the quantity of effect in a given direction. The following points are concluded from above-:
1.A scalar is a physical quantity that has only one magnitude.
2.A vector is a two-dimensional physical quantity that has both magnitude and direction.
3.Arrows can be used to represent vectors, with the length of the arrow indicating the magnitude and the arrowhead indicating the vector’s direction.
4 .A vector’s direction can be determined by referencing another vector or a fixed point (for example, from the riverbank), using a compass (for example, N W), or bearing (e.g. ).
5.The resultant vector is a single vector with the same effect as the constituent vectors combined.
