How Fast Can a Merry-Go-Round Spin Before a Child Slides Off?

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SUMMARY

The maximum speed of a 12-meter diameter merry-go-round before a child with a mass of 30 kg slides off is determined by the static friction coefficient of 0.56. The solution involves calculating the centripetal force required to keep the child on the merry-go-round and using static friction equations to find the relationship between frictional force and normal force. The key equations include those for centripetal acceleration and static friction, which are essential for solving this physics problem.

PREREQUISITES
  • Centripetal force calculations
  • Static friction equations
  • Understanding of normal force
  • Basic physics concepts related to rotational motion
NEXT STEPS
  • Study centripetal acceleration formulas in detail
  • Learn about static friction and its role in circular motion
  • Explore the relationship between mass, force, and acceleration
  • Review examples of rotational dynamics problems
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of rotational motion and static friction in practical scenarios.

cheddahchad
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Homework Statement


A child with mass m = 30 kg is sitting on a 12-m diameter merry-go-round. What is the maximum speed the merry-go-round can travel and the child not slide with a static friction coefficient of 0.56?


Homework Equations



To be honest, I had to miss a day of class because I was sick. I have no idea where to start on this problem. Any help or formulas would be much appreciated!


The Attempt at a Solution



See #2
 
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It's about centripetal force. If you really haven't heard of that or don't know any equations concerning it, search the net. Calculate the centripetal force required to keep the child from spinning off, then use your usual statics equations to determine the frictional force, the normal force, and thus the minimum coefficient of static friction.
 

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