What is the maximum angular velocity for a coin on a turntable without sliding?

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SUMMARY

The maximum angular velocity for a 4.80 g coin placed 11.0 cm from the center of a turntable, without sliding, is determined using the static friction coefficient of 0.770. The equation Ff = FN(u) and the relationship between linear and angular velocity, ω = v/r, are essential in this calculation. The correct approach involves equating the frictional force to the centripetal force required for circular motion. The final calculated angular velocity is approximately 8.27 rad/s, correcting the initial miscalculation of 0.911 rad/s.

PREREQUISITES
  • Understanding of static friction and its coefficient
  • Knowledge of circular motion dynamics
  • Familiarity with the relationship between linear and angular velocity
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of circular motion in physics
  • Learn about the role of friction in rotational dynamics
  • Explore the derivation of angular velocity from linear velocity
  • Practice problems involving static and kinetic friction coefficients
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Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for practical examples of friction and circular dynamics.

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Homework Statement


A 4.80 g coin is placed 11.0 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of us = 0.770 and uk = 0.400.

What is the maximum angular velocity with which the turntable can spin without the coin sliding? (In rad/s)

Homework Equations



Ff = FN(u)
Fa = (mv^2)/r

The Attempt at a Solution



I've always been a little foggy on rotational motion, but for this I converted the grams to kilograms and the centimeters to meters, then set the friction equal to the acceleration:

(.0048)(9.8)(.77) = [(.0048)(v^2)]/.11

Which gave me a v of .911 rad/s. I'm not sure what I did wrong/what I'm missing.
 
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the 'v' you get is the linear velocity, you need to use ω=v/r to get the angular velocity.

(Note: I did not check your answer to see if that is what you did, but your response implied that you put 'v' as the angular velocity)
 

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