What is the Difference Between Vector and Scalar?

[Aartt]

Hi I was reading a physics book and i came to the part where the started to explain vectors and scalars and i got really confuzzled(confused/puzzled) please help

 

[Doc Al]

See: http://www.physicsclassroom.com/class/1dkin/u1l1b.cfm"

 

[Aartt]

thanks so vectors are like more specific than scalars right?

 

[tiny-tim]

Welcome to PF!

Hi Aartt! Welcome to PF!

I wouldn't bother with the difference until you need it.

And when you need it, it'll be clear anyway!

The obvious example of a vector is a force …

it has both a magnitude (a size) and a direction.

Other examples are velocity momentum and acceleration.

Examples of scalars are energy, and the magnitude of any vector.

 

[Delta2]

if u mean by specific that they give more information then you are right.

Vectors have both magnitude and direction, while scalars have only magnitude.

To make it simple, scalars are the real numbers and a physical quantity like temperature is a scalar because we only need a real number to know how big or small the temperature is (and ofc a unit of measurement like Celsius or Fahreneit).

However some other physical quantities like velocity need both a number and a direction that is they need a vector to be represented fully. If we say a car has velocity 100Kmh this is not enough , we got to know also the direction (left or right , up or down, diagonally e.t.c) to where its moving. So to fully represent velocity we can't just use the number 100 (followed by the unit of measurement) but we have to find a way to represent its direction too.

One way to do this is to define 3 unit vectors: i, j and k. Since they are vectors they have magnitude and direction. Unit vectors means that they have magnitude 1. Each of them has a different direction: i is pointing towards left, j towards up and k towards front. Now once we define these unit vectors we can use them to represent the velocity of a car as follows; If the car has 100kmh velocity towards left then we say that its velocity is the vector v=100*i Kmh, if the car has 250kmh velocity towards up then its velocity is the vector v=250*j Kmh.if the car is moving diagonally then the situation become abit more complex but still its velocity can be fully described by a vector of the form v=a*i+b*j where a and b are the proper real numbers. if a car is moving in a zigzag pattern then its velocity vector is changing all the time meaning that both magnitude and direction of velocity changes all the time but still it can be described by a vector of the form v=a(t)*i+b(t)*j+c(t)*k where a(t) , b(t) and c(t) are functions of time.

 

[Kevin_Axion]

The easiest way to imagine vectors and scalars in a physical context (rather than mathematical) is the following:
Vector - this can be seen as an object with a magnitude and direction. For instance, the wind moves with a velocity (the length or magnitude of the vector) and a direction (North East, South West etc.) therefore it is a vector (to be exact a wind current is a vector field).
Scalar - A scalar is a number of the $$\mathbb{R}$$ which for example can define temperature. Temperature is a number (scalar) and it can be assigned at each point in space to make a scalar field.

 

[Aartt]

thanks :D for all the explanations i got the basics but the thing on the bottom of deltas post was O_O confusing but oh well a 6th grader wouldn't understand it.

 

[Delta2]

thanks :D for all the explanations i got the basics but the thing on the bottom of deltas post was O_O confusing but oh well a 6th grader wouldn't understand it.

Yes just forget those at last paragraph i said more than i should and don't make sense if i don't explain some other things first like what is vector addition and functions of time.

 

[Curl]

If you got stuck on vectors and scalars, I'd give up physics.

 

[nocturne-e]

Yes just forget those at last paragraph i said more than i should and don't make sense if i don't explain some other things first like what is vector addition and functions of time.

Lol - that stuff is like.. AP level.


@Curl: Seriously? Trying to discourage an 11 year old from learning physics? That's beyond lame.

 

[Aartt]

what is AP?

 

[Math Is Hard]

Advanced Placement:
http://en.wikipedia.org/wiki/Advanced_Placement

 

[Vagn]

what is AP?

I'm not American myself so I can't give you much information, but what I understand it to be is a course taken in High School which is classed as being equivalent to a college course.
More information from http://en.wikipedia.org/wiki/Advanced_Placement_Program" .

 

[nocturne-e]

what is AP?

There are generally three levels of course in many public high schools across America (I have no idea about the Candian system.)

Regular
PreAP
and AP

PreAP classes are harder than regular class but both are still only high school level courses. AP classes are classes taken in your high school which should be college level but may or may not be. You can get college credit for these classes by taking a test at the end of the year. Do well and many colleges accept credit for that course.

Basically, the i, j, k notation Delta was referring to will not be used in your class because it is college level material. :)

 

[Kevin_Axion]

I'm certain that I will learn everything that an AP student studies, except possibly grade 12 curriculum. My theology teacher told me she was teaching gifted students in grade 5 and they were learning about grade 11 mathematics and sciences.

 

[Phrak]

I don't know what a scalar is. Is there a common definition or does it change with context.

Is it constant over general coordinate transformations?

Is a pseudo scalar a scalar?

Is a function a scalar?

 

[nocturne-e]

I don't know what a scalar is. Is there a common definition or does it change with context.

Is it constant over general coordinate transformations?

Is a pseudo scalar a scalar?

Is a function a scalar?

A scalar is basically something that has magnitude (length) but no direction. Maybe examples will help:

Speed is a scalar. Speed cannot be negative because scalars do not indicated a direction. If two objects were moving in opposite directions but both at 5 m/s, they would have the same speed.

Velocity, however, is a vector. In the case of the two objects, one object will have +5 m/s velocity while the other will have a velocity of -5 m/s.

Examples of scalars: time, speed, mass, temperature, etc.
Examples of vectors: force, velocity, torque, etc.