What is the circumference of the track?

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SUMMARY

The discussion centers on calculating the circumference of a circular track given a runner's speed of 8.50 m/s and an acceleration of 1.03 m/s². Participants clarify that the acceleration mentioned is centripetal acceleration, and the relevant equation for this scenario is a = v²/r. By rearranging this equation to find the radius (r), users can then compute the circumference using the formula C = 2πr.

PREREQUISITES
  • Centripetal acceleration concepts
  • Understanding of circular motion equations
  • Basic algebra for rearranging equations
  • Knowledge of the constant π (pi)
NEXT STEPS
  • Study the derivation of the centripetal acceleration formula a = v²/r
  • Practice problems involving circular motion and centripetal acceleration
  • Learn how to apply the circumference formula C = 2πr
  • Explore real-world applications of circular motion in physics
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Students studying physics, educators teaching circular motion concepts, and anyone interested in applying mathematical principles to real-world scenarios.

Brittykitty
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A student runs at a speed of 8.50 m/s on a circular track. If she accelerates a 1.03 m/s2, what is the circumference of the track?


8.5m/s*1.03m/s?
 
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The wording of the problem implies that the velocity of the girl is a constant and therefore the acceleration referred to is centripetal acceleration. There is a nice equation that expresses the relationship between radial acceleration (centripetal acceleration), velocity and the radius for motion in a circle. So all you need to do is use that to find the radius and use C = 2 \pi r to compute the radius.
 
Last edited:


Thanks! :) so it would be:

2(3.142)14?
 


Brittykitty said:
Thanks! :) so it would be:

2(3.142)14?

No, I don't get that at all. The equation I have in mind is a = \frac{v^2}{r}. That will allow you to calculate r.
 
Last edited:


That's a v squared. It doesn't come out on my computer screen.
 

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