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

AI Thread Summary
To determine the maximum angular velocity of a coin on a turntable without sliding, the static friction force must equal the centripetal force required for circular motion. The coin's mass is 4.80 g, and it is positioned 11.0 cm from the center, with a static friction coefficient of 0.770. The equation used involves setting the frictional force equal to the centripetal force, leading to the calculation of linear velocity. The conversion from linear to angular velocity is essential, using the relationship ω = v/r. The correct maximum angular velocity can be derived from these calculations, ensuring all units are consistent.
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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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