Angular motion problem (wheels on a car coming to a stop)

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SUMMARY

The discussion centers on calculating the number of revolutions made by car tires as the vehicle decelerates from 12.0 m/s to a stop with a constant deceleration of 1.90 m/s². The initial calculations correctly determine the stopping distance as 37.89 meters using the equation Vf² = Vi² + 2ad. However, the confusion arises in converting this distance into revolutions, where the correct method involves dividing the stopping distance by the tire's circumference, calculated as 2.5137 meters. The final result is approximately 15.076 revolutions, which matches the initial calculation but may not be accepted due to formatting issues in submission.

PREREQUISITES
  • Understanding of kinematic equations, specifically Vf² = Vi² + 2ad
  • Knowledge of tire circumference calculation using the formula 2πr
  • Familiarity with unit conversions, particularly between meters and revolutions
  • Basic grasp of physics concepts related to motion and deceleration
NEXT STEPS
  • Review the application of kinematic equations in real-world scenarios
  • Learn more about tire dynamics and the impact of radius on performance
  • Explore common pitfalls in physics homework submissions, especially regarding significant figures
  • Investigate online homework platforms for formatting requirements and common errors
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Students studying physics, particularly those focusing on motion and kinematics, as well as educators looking for examples of real-world applications of these concepts.

xregina12
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The driver of a car traveling at 12.0 m/s applies the brakes and undergoes a constnant decelertion of 1.90m/s^2.
How many revolutions does each tire make before the car comes to a stop assuming that the car does not skid and that the tires of radii of 0.40 m? answer in units of rev.

I used the equation Vf^2=Vi^2+2ad
0=144+2(-1.90)(d)
d=37.89meters
d=r(θ)
θ=37.89/0.40=94.725 radians
revolutions=94.725/(2pi)=15.076 revolutions.
However, I did not get a correct answer. Can anyone help? Did I do this the right way?
 
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You've worked out the distance it takes to stop correctly, but I don't follow your working after that. You know the radius of the tyre is 0.4m, so it's circumference = 2Pi*0.4=2.5137. The car stops in a distance of 37.89 meters, so the number of revolutions is just the distance it takes to stop divided by the circumference of the tyre. Hope that helps.
EDIT: Actually looking at that method I get the same answer as you, so I'm not sure why that's not the correct answer. If this is from an online homework site are you entering the correct number of decimals?
 
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