Thursday, June 16, 2022

# How To Draw A Vector Diagram

## How To Draw A Free Body Diagram

Drawing Scaled Vector Diagrams

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A free-body diagram is a visual representation of an object and all of the external forces acting on it, so to draw one you’ll have to have this information calculated. They are very important for working in engineering or physics problem solving since drawing them helps you to understand what is going on in a problem. A free-body diagram can be drawn very simply, with squares and arrows, or you can make it much more complex. The only requirement is that you or someone else looking at it should be able to understand what the diagram is telling.

A free-body diagram is a representation of a certain object showing all of the external forces that acts on it. FBDs are very helpful in engineering and physics problem solving.

## Determining The Acceleration From A Motion Diagram

Since acceleration is the change in velocity of the car during a corresponding time interval, and we are free to select the time interval as the time interval between exposures on our multiple-exposure photograph, we can determine the acceleration by comparing two successive velocities. The change in these velocity vectors will represent the acceleration.

To determine the acceleration,

• select two successive velocity vectors,
• draw them starting from the same point,
• construct the vector that connects the tip of the first velocity vector to the tip of the second velocity vector.
• The vector you have constructed represents the acceleration.

Comparing the first and second velocity vectors leads to the acceleration vector shown below:

Thus, the acceleration points to the left and is therefore negative. You could construct the acceleration vector at every point in time, but hopefully you can see that as long as the velocity vectors continue to point toward the right and decrease in magnitude, the acceleration will remain negative.

Thus, with the help of a motion diagram, you can extract lots of information about the position, velocity, and acceleration of an object. You are well on your way to a complete kinematic description.

## Example : Venn Diagram With Three Sets

Similar to the R programming code of Example 2, we can use the draw.triple.venn function to create a venn diagram with three sets. Note that this time we need to specify three different area values as well as the pairwise intersections and the intersection area of all sets:

 grid.newpage# Move to new plotting pagedraw.triple.venn

grid.newpage # Move to new plotting pagedraw.triple.venn

Figure 3: Triple Venn Diagram.

Note that the VennDiagram package provides further functions for more complex venn diagrams with multiple sets, i.e. draw.quad.venn, draw.quintuple.venn, or the more general function venn.diagram, which is taking a list and creates a TIFF-file in publication-quality.

However, for simplicity well stick to the triple venn diagram in the remaining examples of this R tutorial.

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## Using The Graphical Method Of Vector Addition And Subtraction To Solve Physics Problems

Now that we have the skills to work with vectors in two dimensions, we can apply vector addition to graphically determine the resultant vector, which represents the total force. Consider an example of force involving two ice skaters pushing a third as seen in Figure 5.7.

In problems where variables such as force are already known, the forces can be represented by making the length of the vectors proportional to the magnitudes of the forces. For this, you need to create a scale. For example, each centimeter of vector length could represent 50 N worth of force. Once you have the initial vectors drawn to scale, you can then use the head-to-tail method to draw the resultant vector. The length of the resultant can then be measured and converted back to the original units using the scale you created.

You can tell by looking at the vectors in the free-body diagram in Figure 5.7 that the two skaters are pushing on the third skater with equal-magnitude forces, since the length of their force vectors are the same. Note, however, that the forces are not equal because they act in different directions. If, for example, each force had a magnitude of 400 N, then we would find the magnitude of the total external force acting on the third skater by finding the magnitude of the resultant vector. Since the forces act at a right angle to one another, we can use the Pythagorean theorem. For a triangle with sides a, b, and c, the Pythagorean theorem tells us that

## Using Components To Add And Subtract Vectors

GCSE Physics – Vector Diagrams and Resultant Forces #43

Another way of adding vectors is to add the components. Previously, we saw that vectors can be expressed in terms of their horizontal and vertical components. To add vectors, merely express both of them in terms of their horizontal and vertical components and then add the components together.

Vector with Horizontal and Vertical Components: The vector in this image has a magnitude of 10.3 units and a direction of 29.1 degrees above the x-axis. It can be decomposed into a horizontal part and a vertical part as shown.

For example, a vector with a length of 5 at a 36.9 degree angle to the horizontal axis will have a horizontal component of 4 units and a vertical component of 3 units. If we were to add this to another vector of the same magnitude and direction, we would get a vector twice as long at the same angle. This can be seen by adding the horizontal components of the two vectors and the two vertical components . These additions give a new vector with a horizontal component of 8 and a vertical component of 6 . To find the resultant vector, simply place the tail of the vertical component at the head of the horizontal component and then draw a line from the origin to the head of the vertical component. This new line is the resultant vector. It should be twice as long as the original, since both of its components are twice as large as they were previously.

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## Technique To Draw Relative Velocities Vectors And Diagrams

How do you start drawing a diagram in a problem with relative velocities? I always see my coursemates and my lecturer drawing them in a second, as soon as they read the text, I asked them how they did it, they just couldn’t explain cause it just comes naturally. But to me it’s very hard to figure out how to actually draw them as we are talking about different frames.

For example consider this problem Now I draw this after a while, where $V_$ is the velocity of the boat wrt the ocean, $V_$ is the velocity of the ocean wrt the ground, and $V_$ is the velocity of the boat wrt to the ground. But the diagram, it is quite random really, because I could have easily put the arrows in another order, but with the same direction! So for example I could have put the head of $V_$ where $V_$ starts or other changes.

How do I decide how to put the arrows? In “putting the arrows” I mean, how do I know I have to put $V_$ starting point as the same of $V_$ and not put the head of the first, where the second starts? And what about where the second has its head?

Is it related to the formula $$V_ = V_ + V_$$ ? and if so how? I really struggle everytime to draw these diagrams and it takes me more than half an hour every time..

EDITTo show what I mean here’s my drawing:

## Setting Up Venndiagram Package

In the examples of this R tutorial, well use functions provided by the VennDiagram add-on package for the R programming language. In order to use the functions of VennDiagram, we need to install and load the package first:

 install.packages# Install VennDiagram packagelibrary# Load VennDiagram package

install.packages # Install VennDiagram packagelibrary # Load VennDiagram package

I recommend to have a look at the help documentation of the VennDiagram package. However, in the following examples youll learn how to apply the main functions of the VennDiagram package.

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## Phasor Addition Using Rectangular Form

Voltage, V2 of 30 volts points in the reference direction along the horizontal zero axis, then it has a horizontal component but no vertical component as follows.

• ;Horizontal Component = 30 cos 0o = 30 volts
• ;Vertical Component = 30 sin 0o = 0 volts
• This then gives us the rectangular expression for voltage V2 of:;;30;+;j0

Voltage, V1 of 20 volts leads voltage, V2 by 60o, then it has both horizontal and vertical components as follows.

• ;Horizontal Component = 20 cos 60o = 20 x 0.5 = 10 volts
• ;Vertical Component = 20 sin 60o = 20 x 0.866 = 17.32 volts
• This then gives us the rectangular expression for voltage V1 of:;;10;+;j17.32

The resultant voltage, VT is found by adding together the horizontal and vertical components as follows.

• VHorizontal = sum of real parts of V1 and V2 = 30 + 10 = 40 volts
• VVertical = sum of imaginary parts of V1 and V2 = 0 + 17.32 = 17.32 volts

Now that both the real and imaginary values have been found the magnitude of voltage, VT is determined by simply using Pythagorass Theorem for a 90o triangle as follows.

Then the resulting phasor diagram will be:

Vector Diagram

One of the ways in which representing physical quantities as vectors makes analysis easier is the ease with which vectors may be added to one another. Since vectors are graphical visualizations, addition and subtraction of vectors can be done graphically.

The graphical method of vector addition is also known as the head-to-tail method. To start, draw a set of coordinate axes. Next, draw out the first vector with its tail at the origin of the coordinate axes. For vector addition it does not matter which vector you draw first since addition is commutative, but for subtraction ensure that the vector you draw first is the one you are subtracting from. The next step is to take the next vector and draw it such that its tail starts at the previous vectorâs head . Continue to place each vector at the head of the preceding one until all the vectors you wish to add are joined together. Finally, draw a straight line from the origin to the head of the final vector in the chain. This new line is the vector result of adding those vectors together.

Graphical Addition of Vectors: The head-to-tail method of vector addition requires that you lay out the first vector along a set of coordinate axes. Next, place the tail of the next vector on the head of the first one. Draw a new vector from the origin to the head of the last vector. This new vector is the sum of the original two.

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## Example : Single Venn Diagram In R

Example 1 shows how to draw a single venn diagram, i.e. only one circle. Have a look at the following R code:

 grid.newpage# Move to new plotting pagedraw.single.venn# Create single venn diagram

grid.newpage # Move to new plotting pagedraw.single.venn # Create single venn diagram

Figure 1: Single Venn Diagram in R.

Figure 1 is visualizing the output of the previous R syntax. Note that the previous code contains two steps.

First, we are creating a new plotting page with the grid.newpage function. We should usually do this step before the creation of each venn diagram, because otherwise the venn diagram is just overlaying previously .

Second, we are producing our single venn diagram with the draw.single.venn function. All we are specifying within the function is the size of our area .

## Example : Change Color Of Venn Diagram

In Example 4, Ill show you how to make a venn diagram with colored lines around the circles and a filling color of the circles. The following R code is the same as in Example 3, but in addition we are specifying the line color to be red and the filling color to be blue . Have a look at the output:

 grid.newpage# Move to new plotting pagedraw.triple.venn

grid.newpage # Move to new plotting pagedraw.triple.venn

Figure 4: Venn Diagram with Color.

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## The Graphical Method Of Vector Addition And Subtraction

Recall that a vector is a quantity that has magnitude and direction. For example, displacement, velocity, acceleration, and force are all vectors. In one-dimensional or straight-line motion, the direction of a vector can be given simply by a plus or minus sign. Motion that is forward, to the right, or upward is usually considered to be positive ; and motion that is backward, to the left, or downward is usually considered to be negative .

In two dimensions, a vector describes motion in two perpendicular directions, such as vertical and horizontal. For vertical and horizontal motion, each vector is made up of vertical and horizontal components. In a one-dimensional problem, one of the components simply has a value of zero. For two-dimensional vectors, we work with vectors by using a frame of reference such as a coordinate system. Just as with one-dimensional vectors, we graphically represent vectors with an arrow having a length proportional to the vectorâs magnitude and pointing in the direction that the vector points.

## Phasor Diagram Of A Sinusoidal Waveform

Simple Vector Diagrams | GCSE & IGCSE Maths | AQA, Edexcel, CIE, OCR

The phasor diagram is drawn corresponding to time zero on the horizontal axis. The lengths of the phasors are proportional to the values of the voltage, and the current, at the instant in time that the phasor diagram is drawn. The current phasor lags the voltage phasor by the angle, , as the two phasors rotate in an anticlockwise direction as stated earlier, therefore the angle, is also measured in the same anticlockwise direction.

If however, the waveforms are frozen at time, t;=;30o, the corresponding phasor diagram would look like the one shown on the right. Once again the current phasor lags behind the voltage phasor as the two waveforms are of the same frequency.

However, as the current waveform is now crossing the horizontal zero axis line at this instant in time we can use the current phasor as our new reference and correctly say that the voltage phasor is leading the current phasor by angle, . Either way, one phasor is designated as the reference phasor and all the other phasors will be either leading or lagging with respect to this reference.

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## Example : Specify Different Color For Each Set

We can also specify a different color for each of the sets of our venn diagram. For this task, we need to set the fill argument to be equal to a vector of colors. Each element of this vector is defining the color of one of the circles:

 grid.newpage# Move to new plotting pagedraw.triple.venn)

grid.newpage # Move to new plotting pagedraw.triple.venn)

Figure 5: Different Color for Each Circle.

## How To Draw This Vector Diagram In Latex

I tried tikzpicture, but the arrow is too thin. also, I don’t know how to draw the coordinate system, and put the label at the end of the arrow.

\begin    \draw   --  node $};\end \documentclass\usepackage\usepackage\begin\begin \draw grid ; \draw -- node; \draw -- node; \draw-- node$};  \draw-- node$};\end\end Another simple solution, with pstricks : \documentclass\usepackage\usepackage\usepackage\usepackage\begin\psset\begin%\psgrid \psaxes \psset\psline\uput\mathbf$}\psline\uput\mathbf\$}\end\end

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## Video Further Resources & Summary

If you need further info on the examples of this page, you might want to watch the following video which I have published on my YouTube channel. In the video, I illustrate the R codes of this tutorial.

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## Wikipedia: Historical Archive/how To Draw A Diagram With Microsoft Word

Intro to Vectors and How to Draw Them | Doc Physics
 This page is currently inactive and is retained for historical reference.Either the page is no longer relevant or consensus on its purpose has become unclear. To revive discussion, seek broader input via a forum such as the village pump.

Since Mediawiki now supports svg files, please use tools which can create svg output for vector graphics. For help on the process, see Wikipedia:How to draw a diagram with Inkscape

This tutorial aims to instruct a beginner on the basic principles of vector graphics using Microsoft Word . The basic principles are the same in other drawing programs such as CorelDraw or the free and open source OpenOffice.org. Similar guides are available for OpenOffice.org Writer or OpenOffice.org Draw.

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## Resultant Forces And Vector Diagrams

The following diagram shows how to resolve a force. Scroll down the page for more examples and solutions on resultant forces and resolving forces.

Resultant ForcesVector Diagrams

Resolving Forces

Resolving vectors – Splitting a Force into Components

## Example : Remove Lines From Venn Diagram

The VennDiagram functions provide the possibility to remove the lines around the circles by specifying the lty argument to be equal to blank. Lets do this in practice:

 grid.newpage# Move to new plotting pagedraw.triple.venn, lty ="blank")

grid.newpage # Move to new plotting pagedraw.triple.venn, lty = “blank”)

Figure 7: Venn Diagram without Lines.

## Ordering Aligning And Flipping Objects

If you click on draw, you will be presented with a number of options for manipulating images. Word orders images on top of on another in the order that you draw them. Sometimes however you want to reverse the order of two objects. This can be done by selecting one of the objects and sending it forwards or backwards.

The flip object is self explanatory. It is often very useful to use this feature if you are drawing a symmetrical diagram. Draw the left hand side, join the individual parts together, copy and paste the image, flip horizontally, then align and join. Hey presto! A perfectly symmetrical object.

The align objects option allows you to precisely align two or more objects together.

 File:Centreing an imagepng.png

The reason that you might need to do this is because, when you move an object by dragging it, the objects do not flow smoothly but instead snap to a grid. The grid is there so that on most occasions objects align up, but if for example you want to centre two complex objects, you may find that no suitable grid point exists and it is impossible to drag the objects into the correct position. The image above shows the effect of a snap grid. Each diamond is one grid position away from the last. As you can see it is impossible to get the diamond in the center of the rectangle.

Another way to correctly position the diamond in the true center of the rectangle is by using the Align option.