Maximizing Turntable Angular Velocity with Friction Coefficients

[Mirole]

Homework Statement

A 6.40 g coin is placed 16.0 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of mu_s = 0.890 and mu_k = 0.540.

What is the maximum angular velocity with which the turntable can spin without the coin sliding?

Homework Equations

The Attempt at a Solution

Fnet(x)= n + fs + fg = ma
= fs = ma
Fnet(y)=n+fs+fg=0
= n = mg

ma = mu_s(mg)
.0064m(a) = (.890)(.0064kg * 9.8)
a = 8.722 m/s^2

a=v²/r
8.722=v²/.16
v = 1.181 m/s

I'm supposed to change it to rad/s, but I have no idea on how to do that or even if I did it correctly.

 

[dotman]

Homework Statement

A 6.40 g coin is placed 16.0 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of mu_s = 0.890 and mu_k = 0.540.

...

I'm supposed to change it to rad/s, but I have no idea on how to do that or even if I did it correctly.

It's difficult to say what to do here since the problem statement doesn't actually contain a problem.

 

[Mirole]

Oh, woops, was in a rush and forgot it, sorry.

What is the maximum angular velocity with which the turntable can spin without the coin sliding?

 

[dotman]

Ahhh, ok. I didn't check the numbers, but I think your method is right. Find the centrifugal force where it just begins to slide, and see what velocity that is equal to.

a = u_s * g = v^2/r => v = (u_s*g*r)^1/2,

which is what you did, and got that velocity.

Ok, so to go to radians, you need to convert your radial velocity from m/s to rad/s. So all you have to do is find the relationship between meters and radians-- and of course, this depends on how far away from the center of the circle you are! Here it said you're 16.0 cm from the center, so you can calculate the circumference of that circle (2*Pi*r), and then calculate how many seconds it would take to go that far at the speed you got, and realize that that same distance is equal to 2 Pi radians.

I don't think I explained that very well. It's pretty easy. Basically you know there's 2Pi rads in a circle, and your conversion factor is the circumference of the circle you're talking about.

Hope this helps!

 

[Mirole]

v=rw
1.181=.16w
W=7.38 rad/s

Thanks!