Rolling disk, energy before pure rotational?

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SUMMARY

The discussion focuses on the mechanics of a solid disk transitioning from rotational motion to pure rolling motion on a horizontal surface. The initial rotational energy of the disk is quantified using the formula E = 1/2 Iω², where I represents the moment of inertia and ω the angular speed. The key factor in this transition is the coefficient of friction (u) between the disk and the surface, which influences the distance traveled before pure rolling occurs. The concept of pure rolling is defined as the state where slipping ceases, and the torque due to friction becomes negligible.

PREREQUISITES
  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with the concept of friction and its coefficients
  • Knowledge of energy conservation principles in mechanics
  • Basic grasp of kinematics related to rolling motion
NEXT STEPS
  • Study the relationship between torque and friction in rolling objects
  • Explore the derivation of the moment of inertia for various shapes
  • Learn about the conditions for pure rolling motion in physics
  • Investigate the effects of different coefficients of friction on rolling distance
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Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and energy transformations in rigid bodies.

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Suppose a solid disk of radius R is given an angular speed about an axis through its center and then lowered to a horizontal surface and released, the coefficient of friction between disk and surface is u. What is the distance traveled before pure rolling occurs?



Conservation of Momentum is applied because no net torque.



The work done by the friction of the disk, fx is used to find the distance x travelled. however i do not know which energy has been changed into work done by friction. What is meant by pure rolling? Only translational and rotational? I'm stuck here.
 
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The initial energy of the disc is rotational and is given by -

[tex]E = \frac{1}{2}I\omega ^2[/tex]

Pure rolling starts when the slipping stops, that is, when the torque due to friction is less than a certain value.
 

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