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Finding the velocity for a given centripetal acceleration

  • Thread starter sh86
  • Start date
19
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THE PROBLEM: (my own words) For a rotating circle with radius 2.10cm, the centripetal acceleration on the rim must be 100g. In revolutions per minute, what is the rate of rotation required?

MY SOLUTION:

1. Centripetal acceleration is given by [tex]a_c = \frac{v^2}{r}[/tex] and so [tex]\frac{v^2}{0.021} = 100g \Leftrightarrow v = \sqrt{0.021 \times 100g} \approx 4.54 \frac{m}{s} [/tex]

2. The velocity is given by [tex]v = \frac{2 \pi r}{T}[/tex] (where T is the period) and so the period is [tex]T = \frac{2 \pi r}{v}[/tex].

3. Therefore the frequency is [tex]f = \frac{1}{T} = \frac{v}{2 \pi r} = \frac{4.54\ \frac{m}{s}}{0.132\ \frac{m}{rev}} = 34.4 \frac{rev}{s}[/tex]

4. This is equal to 34.4/60 RPM = 0.57 RPM.

WHY I'M PISSED OFF: The answer is actually 2060 RPM and I have NO idea what I did wrong. I've checked my answer about a billion times...Please help me.


***EDIT*** OMG! I divided by 60 in step 4 rather than multiplied...This is so stupid I spent over an hour on this problem and spent a really long time writing this post. Well uh...I don't have anything left to say.
 
Last edited:

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