# Physical Quantities

How can we distinguish scalars from vectors?If we are given a certain physical quantity how can we justify whether it is scalar or vector?

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jedishrfu
Mentor
vector quantities have direction. think energy (no direction) and momentum (has direction)

The best example I've found useful is the difference between mass and weight. Mass has no directional value only a magnitude which is a scalar. Weight on the other hand has a magnitude as well as a direction (downward) which is a vector.

The best example I've found useful is the difference between mass and weight. Mass has no directional value only a magnitude which is a scalar. Weight on the other hand has a magnitude as well as a direction (downward) which is a vector.
Wrong on multiple levels.
First, both mass and weight are scalar quantities.
Second mass and weight are not the same (even though they are both scalars).

Uh, weight is the force that gravity exerts on an object, so it's definitely a vector.

Nope,
Weight is the magnitude of the force that gravity exerts on an object.
This has been discussed here before.

Muphrid and myself are correct. Weight is the resultant of mass being acted on by gravity. If you have ever taken the course(s) Statics or Physics or Dynamics, etc. you would know that weight is usually directed downward when viewing in a 2-D reference point. And downward means a sense of direction. You can see this here in this statics example problem with three WEIGHTS directed downward.

http://emweb.unl.edu/NEGAHBAN/EM223/sexam3/IMG00001.GIF

They measure the weight of my luggage at the airport because there is a 50lb limit (scalar).
Its weight measured 55lbs (scalar) so I have to pay an additional \$150 dollars (scalar). I fly to Singapore (opposite side of the Earth). How much does my luggage weight now? Would you say that its weight is now negative?

Again...weight has both magnitude AND direction. They measure your luggage using a weighing scale. These work by measuring the amount of displacement seen by the applied load using a spring system. Without a downward direction and magnitude how could there be any displacement? It would just be floating in the air. To keep your bag static the weighing scale with the spring system produces a force in the opposite direction of the luggage. Again Direction and Magnitude = Weight = Vector. That's Newton's third law of motion my friend. And Newton's Second law of motion clearly explains how a force or in other terms weight is a vector.

And depending on the difference in elevation on the earth's surface between Singapore and where you are flying from the difference in the gravitational constant will be minimal so the weight may only change by hundredths of a fractions of a pound.

weight=mass × acceleration= scalar × vector = vector.
displacement= velocity × time = vector × scalar = vector.
distance travel = speed × time = scalar

AlephZero
Homework Helper
They measure the weight of my luggage at the airport because there is a 50lb limit (scalar).
Actually they measure the mass not the weight. The fact that they probably measure it with a device that includes a force transducer is no more relevant than whether you measure a length with a wooden ruler or a laser device with a digital readout.

I fly to Singapore (opposite side of the Earth). How much does my luggage weight now? Would you say that its weight is now negative?
If makes no sense to say that a vector (weight) is "positive" or "negative". You can only describe the components of the vector as positive or negative, and that description only means something when you define the coordinate system(s) you are using.

Vectors quantities are characterized by more than a single number.

When we measure wind velocity (vector) we make two independent measurements:
Wind speed is measured with an anemometer, wind direction is measured with a wind vane.
The result of this measurement are two independent numbers coorsponding to these two measurements.

When we use radar to measure the position of an airplane, our instrument makes three independent measurements:
Range (measuring pulse delay), and bearing (measuring angular position of antenna), and elevation (measuring elevation of antenna).
These three independent measurement provide the three numbers (components) of the position vector.

Scalars quantities are characterized by a single number. Instruments that measure scalar quantities only produce a single number.
A thermometer reads out a single number. When you step onto a bathroom scale, it produces a single number. These are scalar measurements.

Weight is measured with a scale that does not provide any directional information.

When you draw a force vector for a physics problem you are using
a geometric location relative to the center of the earth to determine the direction of the force vector.

Suppose I gave you the following physics problem:
There are two men, each has a weight of 150lbs. One man in New York City, the other man is in London.
What is the sum of their gravitation force vectors?
Determining the force vectors requires both their weight and their locations.
The location, or directional, information cannot be built into the weight since it is only a single number.

I am fully aware that elementary physics classes have a tendency to show weight as a vector.
This does not make it right, it is a misuse of language.

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Actually they measure the mass not the weight...
They are measuring weight. "If your bag exceeds weight or size limits, please ..."

Mass can be inferred from weight because we know what planet we are on.

jbriggs444
Homework Helper
2019 Award
They are measuring weight. "If your bag exceeds weight or size limits, please ..."

Mass can be inferred from weight because we know what planet we are on.
They are measuring mass. The word "weight" that they use means mass in this context. The scales that they use to do the measurement are calibrated using mass standards, not force standards. The legal rules that establish the meaning of the word "weight" or the unit "pound" in this commercial context trace back to a mass standard, not a force standard.

[For use in commerce, a scale is expected to be certified for use in the location where it is installed -- typically by validation against a set of known masses]

Of course if you try to use this commercial interpretation of "weight" on your physics homework, you should expect to have your answer marked as incorrect.

Context matters in language.

russ_watters
Mentor
For an airplane, it is really weight that matters, not mass. Yes, on earth you can interchange them, but if you want to talk about the mass of luggage, you have to convert from weight to mass, then if you want to make use of it, you convert it back to weight. Simpler to keep it as weight.

Is weightless means massless?
The mass remains. Conservation of Mass.
The gravity changes so does the weight.
So weight is vector since it depends on the direction and the magnitude of the acceleration due to gravity.

They are measuring mass.
If this apparatus were measuring mass then I could transport it to the moon or deep space and it would give the same reading right?. Scales measure the magnitude of the gravitation force exerted on a body and display that result as a single number that we call weight.

When most people in everyday conversation say "weight" they are talking about "the magnitude of the weight." To be correct I should say "My weight is 180 pounds in the downward direction." Everyday life doesn't require people to speak correctly. Similarly, in many Spanish-speaking countries the legal name for the speed limit on the road is the "velocidad maxima." The physicist may complain that a velocity hasn't been reported unless its direction has been reported, but when it doesn't affect most people's everyday activities then they don't feel a need to speak perfectly. The importance of correct terminology depends on the job you have to do. Indict a confessed burglar on a charge of robbery and the jury will have to say not guilty, then the average person in the street will wonder why.

jbriggs444
Homework Helper
2019 Award
If this apparatus were measuring mass then I could transport it to the moon or deep space and it would give the same reading right?. Scales measure the magnitude of the gravitation force exerted on a body and display that result as a single number that we call weight.
If this apparatus was based on a spring or a load cell and you transported it to the moon without re-calibrating it in its new place of usage, then it would give hugely erroneous results.

If this apparatus was based on a balance and you transported it to the moon without re-calibrating it, it would likely give reasonably accurate results.

Scales _respond to_ the force exerted on them by the object they are used to measure. That does not entail that they _measure_ that force.

There is an important semantic distinction there. Though it is rather far removed from the question of whether force is a vector.

If this apparatus was based on a spring or a load cell and you transported it to the moon without re-calibrating it in its new place of usage, then it would give hugely erroneous results.
Exactly my point. This is because it is not measuring mass, it is measuring weight.

I don't think that a citation
"see sign at airport"
would be accepted in a paper and, while this is no peer-reviewed journal, I don't think it should be accepted here. There may be valid points about weight as a vector or a scalar, but they should be physics arguments not common usage arguments.

I don't think that a citation
"see sign at airport"
would be accepted in a paper and, while this is no peer-reviewed journal, I don't think it should be accepted here.
One:
Instrumentation and Measurement Technology Conference, 1996. IMTC-96. Conference Proceedings. 'Quality Measurements: The Indispensable Bridge between Theory and Reality'.

Two:
The Oil Viscous Force Measurement System Based on Embedded System.
Measuring Technology and Mechatronics Automation, 2009. ICMTMA '09. International Conference on
Date of Conference: 11-12 April 2009

In both of these papers, weight is a measured scalar quantity (what you would call "common usage").

Now lets see the scholarly, peer reviewed, papers where weight is a vector with multiple components.
By the way, the NASA reference does not count. It is from a link designed for children.

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jbriggs444
Homework Helper
2019 Award
Exactly my point. This is because it is not measuring mass, it is measuring weight.
We do not disagree about the physics of the situation. We appear to be using words differently.

When I talk about a "measurement" I am considering a measuring device in the sense of an indirect measurement -- as an abstract experiment or "black box" that takes an object as input and produces a numeric figure for some parameter of that object as output. That parameter being something like length, width, mass, weight, specific gravity, velocity, composition or whatever.

When you talk about a "measurement", I think that you are considering a measuring device in the sense of a direct measurement -- as an experiment that considers some directly observable aspect of the object and gives a numeric report on that aspect.

Neither definition is "right" or "wrong. They are merely different.

If you ask the butcher to weigh out two pounds of sliced ham, and if his scale is accurate enough and if the local [apparent] acceleration of gravity differs from the nominal [apparent] acceleration of gravity by enough so that the distinction matters then the laws governing commerce will normally require that the scale correctly report the mass of the ham but will not normally require that the scale correctly report the force the ham exerts on the scale.

If, hypothetically, you were to take that scale to a different location where the local acceleration of gravity is greatly different and if you did not re-calibrate the scale in that location then:

One could say that the scale is no longer accurately measuring the mass of the ham (in the sense of an indirect measurement).

One could say that the scale is still measuring the force required to support that ham against the [apparent] force of gravity (in the sense of a direct measurement). [A proponent of direct measurement might also complain that the read-out should properly be calibrated in units of pound-force rather than pound-mass]

Now, now, I think the definition of weight is mixed up here with layman language.

As I was taught, weight in physics is a vector, its SI unit is Newton.
In layman use, weight normally refers to the scalar quantity that we call mass in physics, and the SI unit is gram.