The Importance of Units for Zero Values in Physics

[Hinte]

My teacher recently docked me 6% on a test because I failed to put units on two values that ended up being zero. For as long as I can remember an answer that is zero does not need units. I looked up examples in our textbook and they left units off answers with values of zero as well. I was wondering if the AP Physics test takes off points for no units on a value of zero. If anyone knows firsthand or can link me resources I would be much obliged. Thanks!

 

[Jimmy Snyder]

I don't know. However, I'm sure they don't take points off if you use units. Temperature needs units even when it's zero. Did you point out to the teacher that the book doesn't use units when the result is zero?

 

[Hinte]

Not yet, I plan to tomorrow.

Also the values that were 0 were Potential Electric (Voltage) and Electric Field (N / C)

 

[Mech_Engineer]

As a general rule, I would think you want to include units on a result of zero to provide context for that result. Yes, 0 in = 0 m = 0 miles = 0 LY, but you want to at least constrain the TYPE of unit the result is (e.g. length, area, voltage, etc.).

As an engineer, I would include units on any calculation result regardless of the numerical value of that result. My .02 c.

 

[BobG]

Jimmy makes a valid point that sometimes zero does need units, as it's just another number on a scale of values. For example, if the specific energy of a projectile's trajectory is zero, it doesn't mean the object has no energy. In fact, it means it finally has enough energy to escape the pull of gravity (minimum escape trajectory).

If the 0 means 'nothing there', then you don't need units. In other words, if your distance is zero, it's zero regardless of whether you're measuring in feet, miles, etc.

If the value can be both positive and negative and just happens to be sitting at zero, then you should include the units. 0 degrees Celsius is a lot different than 0 degrees Fahrenheit.

 

[Hinte]

I understand in real life situations. But on strictly academic grounds where the question states, What is the value of the electric field at point x?
E = 0 seems clear. Assuming it is in fact 0.

Basically, does anyone know how the AP tests treats units on a value of zero?

 

[Jimmy Snyder]

My .02 c.

Units are important in the financial world as well. My .02 $.

 

[jhae2.718]

Units are important in the financial world as well. My .02 $.

Not to Verizon...

Personally, it never hurts to include units.

 

[Mech_Engineer]

Units are important in the financial world as well. My .02 $.

Burned!

 

[Jimmy Snyder]

Burned!

That factor of 100 will get you every time.

 

[Mech_Engineer]

That factor of 100 will get you every time.

LOL, it's so true...

 

[Hinte]

I guess i'll just take the hit.

 

[AlephZero]

Putting in the units shows that you know what units the quantity is measured in.

If your answer said that the temperature of something was 0 feet, that deserves no marks even if the "0" was correct, IMO.

 

[BobG]

Putting in the units shows that you know what units the quantity is measured in.

If your answer said that the temperature of something was 0 feet, that deserves no marks even if the "0" was correct, IMO.

It would probably be extreme to mark off points, but if you took the cross product of two parallel vectors and put units on your answer, I'd consider that a lack of knowledge. There's literally no vector there! If you wanted to use the new vector as a reference and tried to measure the angle between it and some other vector via a dot product, your resulting angle isn't going to be 90 degrees - the angle won't exist because your cross product produced no vector. (Of course, using your dot product to find the angle should reflect that since your magnitude of 0 would result in a divide by zero error, but that's beside the point. If you concluded you had a 90 degree angle as soon as you took your dot product, you'd be wrong.)

 

[micromass]

It would probably be extreme to mark off points, but if you took the cross product of two parallel vectors and put units on your answer, I'd consider that a lack of knowledge. There's literally no vector there! If you wanted to use the new vector as a reference and tried to measure the angle between it and some other vector via a dot product, your resulting angle isn't going to be 90 degrees - the angle won't exist because your cross product produced no vector. (Of course, using your dot product to find the angle should reflect that since your magnitude of 0 would result in a divide by zero error, but that's beside the point. If you concluded you had a 90 degree angle as soon as you took your dot product, you'd be wrong.)

But if you take the cross product of two parallel vectors, then you would get a vector: the zero vector. So there is a vector! Fine, there is no angle between the zero vector and the other vectors, but that doesn't mean that you can't take the dot product and that doesn't mean that you can't talk about orthogonality!

As for the OP, if I were the teacher then I would mark it wrong too. 0 meters is not exactly the same as 0 square meters, for example. But if the book does leave off the units, then I wouldn't subtract points for it.

It all comes down to the definition of a unit, and I'm not sure what the mathematical interpretation of a unit is...

 

[BobG]

But if you take the cross product of two parallel vectors, then you would get a vector: the zero vector. So there is a vector!

What direction does it point? To be a vector, it has to have both a magnitude and a direction.

And remember, it has to be perpendicular to those two parallel vectors you took the cross product of.

And, naturally, it must also be perpendicular to those other two parallel vectors you're about to take the cross product of, since that cross product will get you the exact same zero vector.

And it must also be perpendicular to the two parallel vectors you take the cross product of tomorrow.

 

[Jimmy Snyder]

Does this help?

http://en.wikipedia.org/wiki/Null_vector"

 

[micromass]

What direction does it point? To be a vector, it has to have both a magnitude and a direction.

And remember, it has to be perpendicular to those two parallel vectors you took the cross product of.

And, naturally, it must also be perpendicular to those other two parallel vectors you're about to take the cross product of, since that cross product will get you the exact same zero vector.

And it must also be perpendicular to the two parallel vectors you take the cross product of tomorrow.

You're not really saying that the zero vector isn't a vector, are you? Most of linear algebra would be entirely useless if the zero vector was not a vector... Of course, the zero vector does not have a direction, but that's not really important. You could argue that the zero vector has arbitrary direction, but like I said, that's not really the important part.

And of course the zero vector is perpendicular to every vector. The trick is that perpendicular has to measured with the dot product. And the dot product of any vector with the zero vector is 0, hence perpendicular.

We may be a bit confused since I'm not talking about vectors in physics. But even then, I would be greatly surprised if the zero vector is not a vector in physics...

 

[KingNothing]

To answer the OP's question, yes the AP graders will deduct points for not having units, regardless of the magnitude.

 

[Proton Soup]

i have to say, I'm a big unit guy, myself

 

[BobG]

We may be a bit confused since I'm not talking about vectors in physics. But even then, I would be greatly surprised if the zero vector is not a vector in physics...

No, you're right. You should adhere to the laws of mathematics even when using math in physics.

But a zero vector just isn't very useful when applied to the real world - usually so useless it's easy to forget any mathematical definitions that may accompany it. (But it would be a good bar bet.)