Calculating the Maximum Radius of a Rotating Turntable Before a Coin Slips Off

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Homework Help Overview

The problem involves a coin placed on a rotating turntable, specifically calculating the maximum radius from the center before the coin slips off. The turntable rotates at 33.3 rpm, and the coefficient of static friction is given as 0.1. Participants are exploring the relationship between angular speed, linear velocity, and the forces acting on the coin.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the conversion of angular speed from rpm to rad/s and the implications for calculating forces. There are attempts to apply Newton's second law and questions about the definitions of normal force and acceleration. Some participants express confusion about the relationships between angular speed, linear velocity, and centripetal acceleration.

Discussion Status

The discussion is active, with participants offering hints and clarifications regarding the formulas for centripetal acceleration and the relationship between linear and angular quantities. There is recognition of the need to connect frictional forces to the motion of the coin, but no consensus has been reached on the next steps.

Contextual Notes

Participants are navigating through various equations and concepts without complete information on certain variables, such as the exact values for acceleration or velocity. There is an ongoing exploration of how to relate these variables to the forces acting on the coin.

Djbari
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My problem is: A coin is placed on a turntable that is rotating at 33.3 rpm. If the coefficient of static friction is .1, how far from the center of the turntable can the coin be placed without having to slip off?



Am I correct with V= the 33.3 rpms? and that w (angular speed) =1.11 pi rad/s?
not sure where to go from there
 
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33.3 rpm is not a linear velocity, but is just another measure of angular speed. But, yes, you should convert to standard units of rad/s.

Apply Newton's 2nd law to the coin.
 
N = ma
N = m * 1.11 pi rad/s ?
 
Djbari said:
N = ma
N = m * 1.11 pi rad/s ?
(1) What's N?
(2) What forces act on the coin?
(3) What's the acceleration of the coin?
 
N is the pull inward?
but there is friction holding it on the turntable.
acceleration is the 1.11 pi rad/s?

(I'm really struggling with this and appreciate your help)
 
Welcome to PF!

Djbari said:
Am I correct with V= the 33.3 rpms? and that w (angular speed) =1.11 pi rad/s?
not sure where to go from there

Hi Djbari! Welcome to PF! :smile:

(have an omega: ω and a pi: π :smile:)

Yes, you are correct: ω = 1.11π rad/s.

Now, do you know the formula for centripetal acceleration (acceleration in a circle)? :smile:
 
Djbari said:
N is the pull inward?
but there is friction holding it on the turntable.
Hint: There is only one horizontal force acting on the coin.
acceleration is the 1.11 pi rad/s?
That's the angular speed, not the acceleration. Hint: The coin moves in a circle.
 
why is ω - 1.11 π rad/s? thought it is accel?

Do you mean the formula a=v^2/r ?
 
N would be the weight of the coin or m * a?

accel is v^2/r?
 
  • #10
Djbari said:
why is ω - 1.11 π rad/s? thought it is accel?
Linear acceleration has units of m/s^2.
Do you mean the formula a=v^2/r ?
Sure! (You can also use another version of that formula expressed in terms of angular speed.)
 
  • #11
ω = v^2/r ?
 
  • #12
Djbari said:
ω = v^2/r ?

No. If a=v^2/r, then omega must be something else (since omega is not a)

Do you remember the formula for v in terms of r and omega?
 
  • #13
v = r(w)
 
  • #14
Yes, if by r(w) you mean r times w.

If you substitute that expression for v in
a = v^2 / r,
that will help in solving the problem.
 
  • #15
do I know a or v?
 
  • #16
not v. do I know a?
 
  • #17
No, but that's okay.

You have one expression for a in terms of r and w.

Can you get another expression for a, using what you know about friction?
 
  • #18
Hi Djbari! :smile:

I'm confused. :confused:

In your first post, you got it right … you said ω is angular speed:
Djbari said:
w (angular speed) =1.11 pi rad/s?

But later you said acceleration: :confused:
Djbari said:
why is ω - 1.11 π rad/s? thought it is accel?

Do you mean the formula a=v^2/r ?

Anyway … you got two formulas right:
v = ωr

and a = v²/r​

If you combine them, you get a = (ωr)²/r = … ? :wink:

Then use F = ma. :smile:
 
  • #19
I'm not seeing it. I only see a in terms that have t (time) and I don't have t. or in terms with F net or N and I don't have those do I?
 
  • #20
Hi Tiny -Tim,

I didn't see the previous note matching the two equations. I have actually gotten to there but thought it was wrong - when maybe it's just I thought it stopped there. Am I right with
(w*r)^2/r = 3.45...is it rads? How do I put that into F=ma?
 
  • #21
Use what you know about friction and normal forces.
 
  • #22
Friction force = u*m*g ?
 
  • #23
Djbari said:
Hi Tiny -Tim,

I didn't see the previous note matching the two equations. I have actually gotten to there but thought it was wrong - when maybe it's just I thought it stopped there. Am I right with
(w*r)^2/r = 3.45...is it rads? How do I put that into F=ma?

Hi Djbari! :smile:

Where did 3.45 come from? :confused:

r is the unknown.

You have a = ω²r, and ma = F = mµg.

So … ? :smile:
 

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