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Simple question of vocabulary

  1. Oct 22, 2004 #1

    quasar987

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    Hi.

    When you say "The ratio of the period of the r motion to the period of revolution", does it mean

    [tex]\frac{T_r}{T_\theta}[/tex]

    or

    [tex]\frac{T_\theta}{T_r}[/tex]

    ?

    Judging by the words, I would say it's the first one, but I have many mathmatical reasons to think it it's the second one. I would like a confirmation that it means the second one. Thanks a lot.
     
  2. jcsd
  3. Oct 22, 2004 #2
    Think of it this way. Take the general statement "the ratio of a to b is x:y". This means [itex]a:b=x:y[/itex], so [itex]\frac{a}{b}=\frac{x}{y}[/itex]. This makes sense. Say the ratio is 4. You can convert this to ratio form: [itex]4:1[/itex]. If [itex]a:b[/itex] is [itex]4:1[/itex], then if [itex]b=1[/itex], [itex]a=4[/itex], and if [itex]b=2[/itex], [itex]a=8[/itex], and so on...meaning that in general [itex]a=4b[/itex], so [itex]\frac{a}{b}=\frac{4}{1}[/itex]. Hope this is clear.
     
  4. Oct 23, 2004 #3

    quasar987

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    Then there's an error in the book!!
     
  5. Oct 23, 2004 #4

    quasar987

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    Simple question of physics

    Given that the above sentence means in fact

    [tex]\frac{T_r}{T_\theta}[/tex]

    Does the following sentence make sense (in the context of a particle moving under a central (radial) force with angular momentum non nul)

    "If the ratio of the period of the r motion to the period of revolution is an integer, the orbit is a simple closed curved."

    Consider the following simple counter exemple:

    [tex]\frac{T_r}{T_\theta}=2 \Leftrightarrow T_r=2T_\theta \ (1:2)[/tex]

    Meaning after the particle has covered 4 pi rad around the center of force, the radial oscillation has completed one period. How can that make for a simple closed curve? There will necessarily be an intersection. Whereas if it means the opposite,

    [tex]\frac{T_\theta}{T_r}=2[/tex]

    the curve is closed and much simpler has it does not intersect with itself.


    So is it me or there's an error in the book?
     
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