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

[Djbari]

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

 

[Doc Al]

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.

 

[Djbari]

N = ma
N = m * 1.11 pi rad/s ?

 

[Doc Al]

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?

 

[Djbari]

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)

 

[tiny-tim]

Welcome to PF!

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!

(have an omega: ω and a pi: π )

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

Now, do you know the formula for centripetal acceleration (acceleration in a circle)?

 

[Doc Al]

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.

 

[Djbari]

why is ω - 1.11 π rad/s? thought it is accel?

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

 

[Djbari]

N would be the weight of the coin or m * a?

accel is v^2/r?

 

[Doc Al]

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.)

 

[Djbari]

ω = v^2/r ?

 

[Redbelly98]

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?

 

[Djbari]

v = r(w)

 

[Redbelly98]

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.

 

[Djbari]

do I know a or v?

 

[Djbari]

not v. do I know a?

 

[Redbelly98]

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?

 

[tiny-tim]

Hi Djbari!

I'm confused.

In your first post, you got it right … you said ω is angular speed:

w (angular speed) =1.11 pi rad/s?

But later you said acceleration:

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 = … ?

Then use F = ma.

 

[Djbari]

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?

 

[Djbari]

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?

 

[Redbelly98]

Use what you know about friction and normal forces.

 

[Djbari]

Friction force = u*m*g ?

 

[tiny-tim]

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!

Where did 3.45 come from?

r is the unknown.

You have a = ω²r, and ma = F = mµg.

So … ?