Hoop rolling down incline

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SUMMARY

The discussion centers on a physics problem involving a cylindrical hoop with a radius of 10.0 cm and a mass of 0.550 kg rolling down an incline of 18.0 degrees. The total kinetic energy at the base of the incline is calculated to be 9.49 J, with a velocity of 4.15 m/s. The key challenge presented is determining the minimum coefficient of static friction required for the hoop to roll without slipping, necessitating the application of Newton's 2nd law for both rotational and translational motion.

PREREQUISITES
  • Understanding of Newton's 2nd law for rotation and translation
  • Familiarity with concepts of kinetic energy and rolling motion
  • Knowledge of static friction and its role in preventing slipping
  • Ability to draw and interpret free body diagrams
NEXT STEPS
  • Study the principles of rolling motion and the relationship between linear and angular velocity
  • Learn how to calculate the moment of inertia for a cylindrical hoop
  • Research the derivation of the coefficient of static friction in rolling objects
  • Explore advanced applications of Newton's laws in rotational dynamics
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Students in introductory physics courses, particularly those studying mechanics, as well as educators and tutors seeking to enhance their understanding of rolling motion and friction in dynamics.

Zach981
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This a question from my 131 "masteringphysics.com" hw.

A cylindrical hoop has radius 10.0 cm and mass 0.550 kg. It rolls from rest a distance of 5.70 m along a board which is tipped up by an angle 18.0 degrees from horizontal. Regard the hoop as being much thinner (in the radial direction) than its radius.

Parts A and B wanted me to find the total kinetic energy and velocity at the base of the incline, I already did these. KE = 9.49 J and v=4.15 m/s

However part C wants me to:
What minimum value must the coefficient of static friction have if the hoop is to roll without slipping?
I have no idea how to approach this part.
 
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Start by drawing a free body diagram showing all forces acting on the hoop. Then apply Newton's 2nd law for both rotation and translation.
 

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