Acceleration of Cylinder Rolling Horizontally: Analyzing Forces

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SUMMARY

The discussion focuses on the dynamics of a cylinder rolling horizontally on a surface with kinetic friction coefficient μ. The horizontal acceleration is derived as a = μg, leading to the angular acceleration α_z being calculated as α_z = μg/R. However, the book presents a different solution of -2μg/R, prompting a request for clarification on the reasoning behind this discrepancy. Additionally, the discussion addresses a related problem involving the transition from slipping to rolling without slipping, requiring the calculation of the distance the cylinder rolls before slipping ceases.

PREREQUISITES
  • Understanding of Newton's second law (ma = F)
  • Familiarity with rotational dynamics (α = a/r)
  • Knowledge of friction coefficients (kinetic friction μ)
  • Basic principles of rolling motion (rolling without slipping)
NEXT STEPS
  • Study the derivation of angular acceleration in rolling motion
  • Explore the implications of kinetic friction on rolling objects
  • Learn about the transition from slipping to rolling without slipping
  • Investigate the effects of varying surface conditions on cylinder dynamics
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and frictional forces.

Tonyt88
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You have a cylinder (with radius R) rolling horizontally on a surface with kinetic friction of u(mu). I understand that the horizontal acceleration is u*g b/c:

ma = u*(mg)
a = u*g

and then you have

a = r (alpha_z)

thus I'd figure alpha_z is just u*g/R, but the book gives a solution of:

-2 u*g/R

Basically, what's the reasoning?
 
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Also, I have this problem related to this previous problem:

The cylinder is initially slipping completely, so initially omega_z = omega_o but v_x = 0. Rolling without slipping sets in when v_x = R(omega_z). Calculate the distance the cylinder rolls before slipping stops.
 
Cool.

Oh yeah, could you please use the homework posting template? Thanks.
 

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