aommaster Posted June 17, 2005 Posted June 17, 2005 Hi guys! Its been a long time since I've been here. I've been busy with my AS, and arranging a further maths course for me for my A level! Here is my question: In physics, we were taught that there were 6 (which we were then told 7) SI units, which are: m=meters s=seconds K=Kelvin kg=Kilograms mol=moles A=amps and later : cd=candela (a measure for luminocity) My question is: What about measure of angle? We can't use any of the SI units above to shop an angle, which is quite important in mechanics (the physics course where we were taught this). Thanks alot for your help guys!
mezarashi Posted June 17, 2005 Posted June 17, 2005 An angle is in fact dimensionless. An angle is a ratio. For example the ratio of a circles radius to a segment on its circumference. Using sin and cos, the ratio of opp/hyp and adj/hyp respectively.
mezarashi Posted June 17, 2005 Posted June 17, 2005 Yes, radians and degrees are the names of the units given to angles. They nonetheless remain physically dimensionless. I think that he was referring to the SI base units which only consist of the very fundamental concepts in which everything else can be derived from.
mezarashi Posted June 17, 2005 Posted June 17, 2005 ?_? An angle is in fact dimensionless. An angle is a ratio. For example the ratio of a circles radius to a segment on its circumference. Using sin and cos, the ratio of opp/hyp and adj/hyp respectively. And sorry, I just updated my last post.
ydoaPs Posted June 17, 2005 Posted June 17, 2005 how is an angle dimensionless? i don't understand what you mean.
mezarashi Posted June 17, 2005 Posted June 17, 2005 dimension means: distance, time, temperature, or some other fundamental concept as listed by the base SI units. When you calculate velocity for example you must make sure your answer is in units of: meters/second or distance/time. There is a physical quantity associated with it. Angles are different... they have no physical dimensions associated with them. That's why angles can be exponents and you can perform Sin, Cos, Tan on them. What's the meaning of Sin(30meters) or e^30meters. Angles describe ratios, and from the mathematics I have done, is based on the ratio of a circle's radius to its circumference. The concept is dependent on the more fundamental concept of distance, which is already defined in SI.
ydoaPs Posted June 17, 2005 Posted June 17, 2005 the trig funtions are ratios. angles describe rotation. and radians are used in SI, hence the appearnce of [imath]2\pi[/imath] in many formulas.
mezarashi Posted June 17, 2005 Posted June 17, 2005 I'm not denying that radians is an SI unit. It is an SI unit, but it is considered a derived unit as with frequency (per second) or area (square meter). You state that angles describe rotation. Rotation about? Let's use an example, you say a car wheel rotates pi radians. What does this mean? It means that a point on the wheels circumference has just moved a distance of pi*radius length. Surely here the concept of rotation is about a length dimension. It is a ratio. It has moved half of the circle's circumference. The appearance of 2pi in many formulas defines a ratio!! May be to your surprise. I can say that a wheel rotates at a rate of 2pi radians per second or 1 revolution per second. Instead I use 2pi to denote the ratio of the circumference distance traveled by the revolved radius. Segment of circle = (angle)*radius angle = segment length / radius = (distance)/(distance)
aommaster Posted June 17, 2005 Author Posted June 17, 2005 But, isn't radians used in cacluations and formulae, and therefore a base unit? You can't have anything replacing a measure of angle to give the correct answer. Therefore, I would think that, even though it is a ratio, it is also an SI unit.
mezarashi Posted June 17, 2005 Posted June 17, 2005 Hmmm, okay let me make myself clear one more time: radians is an SI unit for angles This SI unit however is not a base SI unit for the reasons I have explained. Non-base SI units can be used in formulas perfectly fine. The base SI units is just the fundamental class that cannot be derived from anything. Everything other SI unit is considered derived from these bases. National Institute of Standards and Technology http://physics.nist.gov/cuu/Units/
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