A problem on rotational mechanics

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SUMMARY

The discussion focuses on a physics problem involving a uniform solid sphere of radius R that rolls without slipping on a rough horizontal surface and then encounters a rough inclined plane with a 60-degree inclination. The objective is to determine the angular velocity 'n' of the sphere as it rolls up the incline in terms of its initial angular velocity 'w'. Key concepts include the conservation of energy and the moment of inertia, represented by the equations L = Iw and K = 0.5Iw². The solution approach suggested emphasizes the application of conservation of energy rather than angular momentum.

PREREQUISITES
  • Understanding of rotational mechanics and angular momentum
  • Familiarity with the conservation of energy principle
  • Knowledge of moment of inertia calculations
  • Basic trigonometry, particularly with angles and inclines
NEXT STEPS
  • Study the conservation of energy in rotational motion
  • Learn about moment of inertia for different shapes, particularly spheres
  • Explore the relationship between linear and angular velocity in rolling motion
  • Investigate the effects of friction on rolling objects
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of rotational mechanics and energy conservation in rolling motion scenarios.

nikhilnagaraj
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Homework Statement


A uniform solid sphere of radius R rolling on a rough horizontal surface without slipping, with an angular velocity 'w' meets a rough inclined plane of inclination 60degrees. The sphere continues to roll up the plane without slipping with an angular velocity 'n' given by ______________ (in terms of w)

(Please refer the attachment for the diagram)


Homework Equations


I GUESS,
L =Iw , K=.5 Iw^2 , I.is moment of inertia.


The Attempt at a Solution


I think this problem requires Conservation of angular momentum , but I do not know how to start or where to apply the principle.
 

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nikhilnagaraj said:

Homework Statement


A uniform solid sphere of radius R rolling on a rough horizontal surface without slipping, with an angular velocity 'w' meets a rough inclined plane of inclination 60degrees. The sphere continues to roll up the plane without slipping with an angular velocity 'n' given by ______________ (in terms of w)

(Please refer the attachment for the diagram)


Homework Equations


I GUESS,
L =Iw , K=.5 Iw^2 , I.is moment of inertia.


The Attempt at a Solution


I think this problem requires Conservation of angular momentum , but I do not know how to start or where to apply the principle.

Welcome to the PF.

Try using conservation of energy instead... :smile:
 

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