Timeline for Simple Harmonic Motion - What are the units for $\omega_0$?
Current License: CC BY-SA 3.0
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| Aug 27, 2012 at 12:48 | comment | added | Physiks lover | which is equivalent to multiplying the lhs by (1/k)k so you're back to 1(degree) = (k= 180/π)(2πr/360)/r where every thing is consistent since the rhs = 1. But the rhs isn't just the ratio of two lengths, you still need k. | |
| Aug 26, 2012 at 23:51 | comment | added | David Z | Sure... on the left you have the number 1, on the right you have the conversion factor $k$. So you multiply $1/k$ over to the left side and relabel it as a unit, namely the degree. That's how the degree is defined. | |
| Aug 26, 2012 at 22:14 | comment | added | Physiks lover | My previous comment wasn't quite correct and I should have said that angle is the ratio of arc-length to radius multiplied by a normalising factor K. You state: 'Incidentally, this also implies that "degree" is just a fancy name for the number π/180". I don't think this is correct because on one side you have the number 1(degree), on the other you have the ratio of two numbers(lengths) where the r's cancel to give $\pi/180$. so you need the conversion factor $k=180/pi$ in $1=k(2\pi r/360)/r$ | |
| Aug 26, 2012 at 17:31 | comment | added | David Z | @Physikslover I don't understand how you're claiming this isn't right. Surely you agree that $r/r = 1$, right? And also $r/r = 1\text{ rad}$ by definition. | |
| Aug 8, 2012 at 21:58 | comment | added | Physiks lover | I don't think this is right. 1 radian and 1 degree are both assigned the number 1, and both defined as the ratio of an arc length to radius, but using different standards for arc-length. The radian uses the radius, the degree uses the circumference divided up into 360 arc-lengths. Since angle = k arc-length/radius, then $k=180/\pi$ takes care of calculating 1 degree correctly for an arc-length = $2\pi r/360$ | |
| Jun 23, 2011 at 18:33 | history | edited | David Z | CC BY-SA 3.0 |
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| Jun 23, 2011 at 18:26 | vote | accept | Hopelessmathmajor | ||
| Jun 23, 2011 at 17:53 | history | edited | David Z | CC BY-SA 3.0 |
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| Jun 23, 2011 at 17:22 | history | answered | David Z | CC BY-SA 3.0 |