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

In summary, the conversation discusses the maximum angular velocity at which a turntable can spin without a 4.80 g coin sliding. The coin has static and kinetic coefficients of friction with the turntable surface of us = 0.770 and uk = 0.400. The relevant equations used are Ff = FN(u) and Fa = (mv^2)/r. The solution involves converting units and using ω=v/r to find the angular velocity, which was calculated to be 0.911 rad/s.
  • #1
Cfem
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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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  • #2
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)
 

What is circular motion?

Circular motion is the movement of an object along a circular path, where the distance from the center of the circle remains constant.

How is circular motion of a coin different from linear motion?

Circular motion is a curved path, while linear motion is a straight line. In circular motion, the object constantly changes direction, whereas in linear motion, the object moves in a single direction.

What causes a coin to undergo circular motion?

In circular motion, there must be a force acting on the object towards the center of the circle. This force is known as centripetal force and can be caused by tension, gravity, or any other force that pulls the object towards the center.

Can a coin undergo circular motion without a centripetal force?

No, circular motion cannot occur without a centripetal force. Without a centripetal force, the coin would continue moving in a straight line instead of following a curved path.

What factors affect the speed of circular motion of a coin?

The speed of circular motion is affected by the radius of the circle, the mass of the coin, and the strength of the centripetal force. Increasing the radius or the mass of the coin will decrease the speed, while increasing the strength of the centripetal force will increase the speed.

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