What is Vector Physics — A concise guide for high school Physics for you

What is the vector physics chapter? And what we learn in this chapter?
Vector physics is one of the most fundamental chapters in high school physics where we learn about Vector and Scalar quantities.
To understand it we have to proceed step by step starting with physical quantity.

The quantity which can be measured is called physical quantity. The physical quantities measured in physics can be divided into two groups, scalars, and vectors.

Scalar and Vector

Scalar Definition: Scalars are physical quantities that have a magnitude only. Examples of scalars are the length, speed, mass, density, energy, power, temperature, charge, and potential difference.

Vector Definition: Vectors in physics are physical quantities that have magnitude as well as direction. Examples of vector quantity are displacement, force, torque, velocity, acceleration, momentum, and electric current.

What is Vector physics — definition, examples, and notation

What is vector physics? Define Vector?

Vectors in physics are physical quantities that not only have magnitude but also direction. Let’s take an example:

The quantity 55 km per hour is a scalar, while the quantity 55 km per hour to the east is a vector.

A vector can be graphically represented by a line with an arrowhead.
The length of the line represents the magnitude of the vector and the direction of the arrowhead indicates the direction of the vector.

Vectors can be denoted in several ways in text, including:

In textbooks, you’ll generally see one of the first two, but when it’s handwritten, you’ll find one of the last two.

Scalars can be added together by simple arithmetic but when two or more vectors are added together then simple arithmetic is not sufficient, as their direction must be taken into account as well.

The addition of vectors gives us the resultant vector. This post is going to cover a wide area of vector physics. Apart from addition, we will gradually cover subtraction of vectors, vector resolution, vector product, vector dot product, vector cross product, etc. If you are looking for vector class 11 content for CBSE, ISC or state boards, you are in right place.

Resultant Vector — Addition of vectors in physics

When two or more vectors are added the resulting sum of the vectors is called the resultant vector or simply the resultant. The resultant vector represents the net effect of the vectors added.

Resultant of Vectors acting in the same line or parallel — what is vector physics

Two or more vectors acting in the same line (same direction or just opposite direction) can be added as if they were scalars.

Here Vectors may lie in the same line or may be parallel to each other.

For example, the sum, or resultant, of the two forces shown in figure (a) below is 500 N acting towards the right.

The resultant of the two forces shown in figure (b) below is 100 N towards right.

Again in figure © below, we added 3 vectors and the sum is 100N towards left.

Resultant of Vectors acting in different directions — scale diagram and formula-based calculation

If the two vectors acting on a body are not acting along the same line then the resultant vector can’t be found so easily as the above-described cases.

This time the resultant can be found by either using a scale diagram(geometrical) or by calculation using vector addition formula.

Scale diagram:
A scaling factor is decided first (say 100 N of force =1 cm). Accordingly, 2 straight lines representing 2 vectors are drawn with specific ‘scaled’ length and direction.

The two vectors are drawn ‘head to tail’. This completes 2 sides of the triangle. The 3rd side is drawn now that closes the triangle.

This side represents the resultant vector. Its direction is taken from the Tail of the first vector to the head of the second vector. This is called the Law of Triangle for Vector Physics or Triangle law of vector addition.

Triangle law of vector addition — what is vector physics

If two vectors are denoted by two sides of a triangle in sequence, then the third closing side of the triangle, in the opposite direction of the sequence, represents the sum or resultant of the two vectors in both magnitude and direction.

How to solve vector problems in physics — find resultant of 2 vectors

In the above diagram (a) please find two vectors A (400 N) and B (300 N).
For simplicity, we have taken them at a right angle to each other.
Also pls note the directions of the 2 vectors from the arrowheads they have.

We have to find out the resultant of A and B. We will try both geometrical (scaling) way and the calculation using formula.

Finding the Resultant vector using a Scale diagram — what is vector physics

setup

In diagram (a) above we see 2 vectors A and B.

For simplicity of calculation at this moment we have taken 2 vectors at a right angle.

The magnitude of A and B vectors are 400 N and 300 N respectively.

We have to take a convenient scaling system, like for every 100 N in this case, we may take 1 cm.

Steps

Using this scaling (100 N = 1 cm) factor, we will draw a scale diagram in both magnitude and direction. We use a ruler and protractor.

See fig b now.

First, say we draw a line of 4 cm length using a ruler, representing 400 N and the direction is west to east as per the direction of vector A.

The arrowhead of vector A would be the point where tail of vector B will reside.
Accordingly, vector B is drawn as a line of length 3 cm (for 300 N) at a right angle with respect to the ‘vector A’ line and it stands at the head of the ‘vector A’ line.

Thus head to tail scaling representations are made for vector A and B.

We get the resultant vector R as we draw the line starting from the initial point(tail of vector A) and ending at the final point(head of vector B) that closes the triangle (Figure b).

If properly drawn, we will get the length of this line as 5cm which represents 500 N as per scaling factor used.

The direction of the resultant can be found by measuring angle θ between the resultant R and vector A. We use a protractor to measure the angle.

In this case, θ = 37°.

So we get the resultant of vector A and B which is 500 N making an angle of 37° with vector A.

Finding the resultant with formula of Pythagorean theorem — vector physics

The resultant R of the two vectors in figure (a) can also be found by calculation.
For this special case, when two vectors are at right angle, we can use the Pythagorean theorem to find out the R.

[In other cases when the angle between two vectors is different, we use a different formula. We will discuss this later in this tutorial.]
So, in this case, using Pythagorean theorem,
resultant = √(400 + 300 ) = √250000 = 500 N

The direction of R can be found in the following manner:
tan θ =300/400= 0.75
So, = 36.9°

Always we should choose a sensible scale when drawing scale diagrams of vectors.

How to solve vector addition problems — when vectors are not at the right angle

Solution — Using Scale diagram hands-on approach @ Vector physics lab

Here we have adopted a hands-on approach as we take at our vector physics lab.

Say, a block is resting on a surface. Two forces A and B are working on the block as shown above.

The magnitude of force A is 400 N and the magnitude of force B is 350 N.

[Read More…]

Originally published at https://physicsteacher.in on June 22, 2019.

NIT Grad & IT prof. Writes and teaches HS physics. A motivational speaker and an active blogger with multiple niches. With lots of stories to tell.

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