Meaning of Multiplication and Division in Physics

[ergospherical]

They have the same dimensionality. Not the same units.

Having equal dimensionality implies they can be expressed in the same units…

It is usually the Nm (Newton metre)

 

[jbriggs444]

Having equal dimensionality implies they can be expressed in the same units…

I distinguish between units and dimensions.

 

[ergospherical]

I distinguish between units and dimensions.

Indeed, because they are different things… (loosely, dimensionality is associated with an [infinite] set of possible units…)

Nonetheless torque and energy share the same set of units

dW = F . dr
t = r x F

 

[jbriggs444]

Indeed, because they are different things… (loosely, dimensionality is associated with an [infinite] set of possible units…)

Nonetheless torque and energy share the same set of units

dW = F . dr
t = r x F

With radians (arguably a dimensionless unit) as a conversion factor between torque applied and energy expended through a unit rotation angle).

 

[hutchphd]

This discussion has given me a headache. But it did remind me of a favorite quote (seems apropos):

"Under capitalism, man exploits man. Under communism, it's just the opposite."

John Kenneth Galbraith

.

 

[dromarand]

Interesting conversation, I think that the criterion with unit is very important.I actually think that after you have this fundamental defining formulas such as average speed=total distance/total time, you can obtain other formulas such as Galileo's formula(v square=v0 square+2ad) just doing the math,without any trouble. But,in my view, the problem is still with this fundamental equations. For instance, why the speed is distance per time and not distance multiplied with time? I see the proportionality between time and distance (if speed is constant), but I still cannot perfectly understand this problem.

The ideal model of the discussed experiment assumes that the first falling snowflakes (constant vertical precipitation velocity, constant density) touch the ground at the moment of starting the measurement of the dozer movement (horizontal, uniform rectilinear motion).
Which dozer, under the same conditions, will pick up more snow; the one who traveled 40 m in 30 s, or the one who traveled 50 m in 20 s?
The entire experience (with two dozers) repeated at a other snowfall speed will not change which of them will sweep more snow.
Imagine a right triangle against the falling snow. The triangle moves vertically down with the snow. One cathetus is the distance s, the other cathetus - height is proportional to the time t. The movement of the point of intersection of the hypotenuse with the ground line is the movement of the dozer. The precipitation pushing capacity x=st/2 could be a physical quantity, the measurement unit of which would be a meter-second.

 

[sophiecentaur]

I distinguish between units and dimensions.

Different animals entirely; I agree
'They' had to invent dimensional analysis to take care of this and other problems. As far as I know, the US has to accept the same convention for dimensions as we use in UK, despite their continuing love affair with feet.

 

[jbriggs444]

Different animals entirely; I agree
'They' had to invent dimensional analysis to take care of this and other problems. As far as I know, the US has to accept the same convention for dimensions as we use in UK, despite their continuing love affair with feet.

Feet go up to twelve. That's two more.

With apologies to Spinal Tap.

 

[sophiecentaur]

Feet go up to twelve. That's two more.

With apologies to Spinal Tap.

I wonder where that movie would be now without the volume control gag.

One afternoon, I watched it with my teenage son in a cinema in Brighton (UK). There were just three of us in the audience; Tom and I and a little old man on the other side of the gangway. Without the '11' gag, he would probably not have been there.

 

[Herman Trivilino]

Why any quantities can multiply or divide,contrary to adding and subtracting.

Let's take a simple equation from rectilinear motion: $\Delta x=vt$. In other words, displacement equals the product of the velocity and the time. You know that multiplication is a series of additions. So if you have a velocity of $2 \ \mathrm{m/s}$ for 3 seconds you travel 2 meters in the first second, 2 meters in the next second, and finally 2 meters in the third second. $2 \ \mathrm{m}$+$2 \ \mathrm{m}$+$2 \ \mathrm{m}$=$6 \ \mathrm{m}$.

Note that you never add two quantities with different units.

 

[sophiecentaur]

A question that gets my mind going in ever decreasing circles is "what is it about three that allow it to be applied to so many quantities?" . There's a 'threeness' that is outside the physical world. We do our three times table but when we explain it to a child we talk about three apples and four boxes of three apples etc.

 

[jbriggs444]

A question that gets my mind going in ever decreasing circles is "what is it about three that allow it to be applied to so many quantities?" . There's a 'threeness' that is outside the physical world. We do our three times table but when we explain it to a child we talk about three apples and four boxes of three apples etc.

There are only four many numbers. One, two, three and many.

 

[hmmm27]

There are only four many numbers. One, two, three and many.

I haven't the reference material on hand, but isn't it "One, Two, Many, Lots" ?