Snooker ball rolling, frictional effects, moment of inertia.

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SUMMARY

The discussion focuses on the dynamics of a billiard ball transitioning from sliding to rolling on a table, specifically analyzing the effects of friction and the moment of inertia. The ball, with mass m and radius a, experiences a frictional force of magnitude qmg. The moment of inertia about a diameter is given as 2/5 ma². The key conclusion is that the ball will begin to roll when the acceleration due to friction equals the required acceleration for rolling without slipping, which can be calculated using the provided equations and parameters.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concept of frictional forces
  • Knowledge of moment of inertia calculations
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the relationship between linear acceleration and angular acceleration in rolling motion
  • Learn how to apply Newton's second law to rotational systems
  • Explore the role of static and kinetic friction in motion transitions
  • Investigate the effects of different coefficients of friction on rolling behavior
USEFUL FOR

Physics students, educators, and anyone interested in the mechanics of motion, particularly in understanding the transition from sliding to rolling in rigid bodies.

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Homework Statement



A billiard ball (of mass m and radius a) is struck by a cue and moves off with initial speed u, sliding (without rotation) along the table top. After what time will the ball roll rather than skid, if the frictional force between the ball and the table has magnitude qmg. (Recall that the moment of inertia of the ball about a diameter is 2/5 ma^2)

Homework Equations






The Attempt at a Solution


I see at the point when the ball begins to roll the ball will have an acceleration corresponding to a force that is less than the frictional force between the ball and table. But I am unclear on how to proceed on finding the time at which this occurs and where the moment of inertia comes into this. Any guidance much appreciated.
 
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its ok i think i got this one, found it here: http://www.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_4.html
 
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