Calculating Angular Acceleration and Stopping Time for a Rolling Train

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SUMMARY

The discussion focuses on calculating the angular acceleration and stopping time of a toy train rolling on a horizontal track with a diameter of 1.8 meters and a coefficient of rolling friction of 0.11. The angular acceleration can be determined using the formula for centripetal acceleration, a = v²/r, where v is the initial angular speed of 31 rad/s. To find the stopping time, one must equate the centrifugal force to the normal rolling friction force, simplifying the problem to a linear track analysis using the track's circumference for distance calculations.

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  • Understanding of angular motion and acceleration
  • Familiarity with the concepts of centripetal acceleration
  • Knowledge of rolling friction and its coefficient
  • Basic algebra for manipulating equations
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  • Learn how to apply the equations of motion for rolling objects
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Homework Statement


A toy train rolls around a horizontal 1.8 m diameter track. The coefficient of rolling friction is 0.11.

What is the magnitude of the train's angular acceleration after it is released?
How long does it take the train to stop if it's released with an angular speed of 31 ?

Homework Equations


a=v2/r perhaps


The Attempt at a Solution


I am not even really sure how to begin this problem. I am pretty sure it has something to do with centripetal acceleration but I really just have no idea where to begin. Any help would be great. Thanks!
 
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Your on the right track (no pun intended).

Can you equate the centrifugal force to the normal rolling friction force?
 
The question deliberately avoids you having to worry about it being a circular track. You just pretend it's a straight track and use circumference=2*pi*radius to convert the distances.
 

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