Circular motion Involving Static Friction

[Jtappan]

Homework Statement

A coin is placed on a turntable that is rotating at 45.0 rpm. If the coefficient of static friction between the coin and the turntable is 0.1, how far from the center of the record can the coin be placed without having it slip off?
______ cm

Homework Equations

F = mew(s)N

The Attempt at a Solution

I have no idea how to solve this one...which information is implied? Any help?

 

[Anadyne]

The coin is moving in a circle right? Which means that there is some sort of centripetal force acting on the coin. What force is it?

 

[ogb p]

I would approach this problem by first defining the variables and equations involved. In this case, we have a coin placed on a rotating turntable, so we can use the equation for circular motion, which is F = m*r*w^2, where F is the centripetal force, m is the mass of the coin, r is the distance from the center of rotation, and w is the angular velocity (in radians per second).

Next, we have the coefficient of static friction, which is a measure of how much force is needed to keep the coin from slipping off the turntable. The equation for static friction is F(s) = mew(s)*N, where mew(s) is the coefficient of static friction and N is the normal force (in this case, the weight of the coin).

To solve for the distance from the center of rotation, we can set these two equations equal to each other and solve for r:

F = F(s)
m*r*w^2 = mew(s)*N

We know the angular velocity (45.0 rpm) and the coefficient of static friction (0.1), but we need to find the normal force. The normal force is equal to the weight of the coin, which we can calculate using the mass of the coin (which is not given in the problem). Let's assume the coin has a mass of 1 gram, so the weight would be 0.001 kg * 9.8 m/s^2 = 0.0098 N.

Substituting this value into the equation, we get:

m*r*w^2 = mew(s)*N
m*r*w^2 = mew(s)*0.0098 N

We can now cancel out the mass (m) on both sides of the equation, leaving us with:

r*w^2 = mew(s)*0.0098

We know the angular velocity (w) is 45.0 rpm, but we need to convert it to radians per second. We can do this by multiplying it by 2*pi/60, which gives us 4.71 radians per second.

Substituting this value into the equation, we get:

r*(4.71 radians/s)^2 = 0.1*0.0098
r*22.17 = 0.00098
r = 0.00098/22.17
r = 0.