No slip wheel, distance covered, find revolutions

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SUMMARY

The problem involves calculating the number of revolutions made by a bicycle wheel with a radius of 0.400 m over a distance of 3.0 km. The correct formula for determining the number of revolutions is given by the equation: number of revolutions = distance / (2 × π × radius). Applying this, the calculation yields approximately 119.4 revolutions, which contradicts the provided answer choices. The confusion arises from misinterpretation of units and the calculation process.

PREREQUISITES
  • Understanding of basic geometry, specifically the circumference of a circle.
  • Familiarity with the mathematical constant π (Pi).
  • Ability to convert units, specifically kilometers to meters.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Review the concept of circumference and its application in circular motion.
  • Learn about unit conversions, particularly between kilometers and meters.
  • Explore the relationship between distance traveled and revolutions in rotational motion.
  • Practice similar problems involving circular motion and revolutions for better comprehension.
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Students studying physics, mathematics enthusiasts, and anyone interested in understanding the principles of rotational motion and unit conversions.

jehan4141
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The radius of each wheel on a bicycle is 0.400 m. The bicycle travels a distance of 3.0 km. Assuming that the wheels do not slip, how many revolutions does each wheel make?

This problem seems so simple but none of the possible answers available seems correct.

My work

r = 0.4 m
x = 3 km = 3000 m

# of revolutions = x / [(2)(Pi)(r)] = 3000 / (2 x 3.14 x 0.4) ~119.4 m?

-------------------------
Below are the answers to choose from

8.4 × 10-4 revolutions


1.2 × 103 revolutions


Since the time of travel is not given, there is not enough information for a solution.


6.0 × 103 revolutions


2.4 × 102 revolutions
 
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I think you slipped a decimal place in your calculation. Also, revolutions are not measured in units of meters.
 
that is the weirdest thing. i think i calculated that about 4 times before getting frustrated and posting here. thank you so much!
 

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