Damn you mathematicians

[Duke]

So you don't like angles not having dimensions?

[MelchyBeau]

Don't angles by definition have 2 dimensionality. Though in physics it is best to define it in R3. Otherwise, saying you are going to rotate something does not make sense unles you know by what axis you are going to rotate something about

[Neuge]

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Don't angles by definition have 2 dimensionality. Though in physics it is best to define it in R3. Otherwise, saying you are going to rotate something does not make sense unles you know by what axis you are going to rotate something about

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Angles measure the difference in slope between two lines or vectors, which is dimensionless.

[Phil153]

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'cause s doesn't have units length*angle. Or at least that's my guess.

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Bingo. The expression is dimensionally incorrect. I [censored] HATE THAT [censored].

Me for 1/2 the semester: UNITS UNITS UNITS UNITS!

Me 1/2 way through the semester: Uh, except . . .

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Borodog,

You should let the market decide the units, rather than imposing your centrally planned bureaucratic monopolist unit system.

Off topic non sequiturs about the evil government are annoying, no?

[flipdeadshot22]

I don't understand. radians are dimensionless units of angular displacement. what can be so hard about teaching a bunch of 14 year olds about this? I didn't have much difficulty in learning about the concept of radians (not trying to brag.) Just break down the scientific justification of the radian measurement to these kids, i'm sure they'll follow.

[bxb]

All the formulas are the same as they are for regular kinematics cept different letters.

[bluesbassman]

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'cause s doesn't have units length*angle. Or at least that's my guess.

[/ QUOTE ]

Bingo. The expression is dimensionally incorrect. I [censored] HATE THAT [censored].

Me for 1/2 the semester: UNITS UNITS UNITS UNITS!

Me 1/2 way through the semester: Uh, except . . .

[/ QUOTE ]

I still don't understand what is your problem with the given expression. That must make me pretty dumb, since I "do" rotational kinematics for a living. (I design attitude control systems for spacecraft.)

FWIW, where possible, I prefer to express 3-dimensional rotational kinematics in terms of the rate of change of a quaternion: (see equation 9, p. 14)

Quaternion dynamics

[Borodog]

Ok, I shouldn't have said "dimensionally incorrect." However, just because angles are physically dimensionless does not imply that they are unitless. The very fact that the expression s = r*theta is only "correct" for one system of angular measurement tells you that there is monkey business going on.

I stress to my students over and over that they should pay attention to the units, that the units will not let them down. Until we get to rotational kinematics, and the units of radians suddenly vanish for little better than handwaving reasons. This could all have been avoided by choosing a constant of proportionality of 1 radian^-1 rather than simply 1.

[Borodog]

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I don't understand. radians are dimensionless units of angular displacement. what can be so hard about teaching a bunch of 14 year olds about this?

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They grow college kids young where you live.

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I didn't have much difficulty in learning about the concept of radians (not trying to brag.) Just break down the scientific justification of the radian measurement to these kids, i'm sure they'll follow.

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You are missing the point. I beat them over the head with units for 6 weeks, and then suddenly tell them, "Oh, yeah, those units of radians? They magically disappear."

[Borodog]

Phil,

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You are ignoring this troll.

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Congratulations.