# Particle sliding off turntable - find friction

## Homework Statement

A turntable rotates at 78 rev/min
A particle on the turntable is located 0.14 m from the center of the rotating turntable
The particle on the turntable has a mass of 16 g.

Calculate the force of friction which keeps it from sliding off

## Homework Equations

$$f_s = m(v^2/r)$$
$$a_c = r\omega^2$$
$$F=ma$$

## The Attempt at a Solution

I don't really understand this one. What is the force that would be pushing the particle of the turntable in the first place? Would it be the angular velocity or the tangential velocity? What is the difference between the two?

I calculated the angular velocity to be:

$$(\frac{78rev}{min})(\frac{1 min}{60s}) * 2\Pi rad = \frac {8.17 rad}{s}$$

And calculated the speed of the particle to be:

$$.14m * \alpha = 1.1438 m/s$$

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Chi Meson
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## Homework Statement

A turntable rotates at 78 rev/min
A particle on the turntable is located 0.14 m from the center of the rotating turntable
The particle on the turntable has a mass of 16 g.

Calculate the force of friction which keeps it from sliding off

## Homework Equations

$$f_s = m(v^2/r)$$
$$a_c = r\omega^2$$
$$F=ma$$

## The Attempt at a Solution

I don't really understand this one. What is the force that would be pushing the particle of the turntable in the first place? Would it be the angular velocity or the tangential velocity? What is the difference between the two?
There is NO force that would be pushing the particle off the turntable; inertia (the fact that it is moving) would cause the particle to travel in a straight line which would leave the turntable. A force is necessary to change the straight line motion and make it circular motion. In perfect circular motion, the net force is a centripetal force (find that formula) that causes the object to NOT travel in a straight line.

Some force (in this case friction) must step in to be the required centripetal force.

Angular velocity (omega) is the rate of rotation in "radians per second." You are given "revolutions per minute" so you need to convert. Tangential velocity (v) is the linear speed of the particle ("tangent" is the direction that is perpendicular to the radius at a point on a circle).

you don't need the torque formula.

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Well there are two ways to look at it: centripetal and centrifugal. I'll explain centripetal one since some people get mad about centrifugal forces. In order for the particle to be moving in a circle, it needs a centripetal force. Figure out what forces are acting on the particle and do a free body diagram. The net force must equal the required centripetal force. Solve for friction.

Tangential velocity is just the velocity of the particle in m/s. It gets its name because it is directed tangent to the circle the particle is traveling in.

Angular velocity is in radians/s and is the rate of change of the angle between some arbitrary radius and the radius that the particle is on. They are related by the follwing equation

$$\omega =\frac{v}{r}$$

where omega is the angular velocity, v is the tangential velocity, and r is the radius of the motion.

Neither of these, however, are forces.

There is NO force that would be pushing the particle off the turntable; inertia (the fact that it is moving) would cause the particle to travel in a straight line which would leave the turntable. A force is necessary to change the straight line motion and make it circular motion. In perfect circular motion, the net force is a centripetal force (find that formula) that causes the object to NOT travel in a straight line.

Some force (in this case friction) must step in to be the required centripetal force.

Angular velocity (omega) is the rate of rotation in "radians per second." You are given "revolutions per minute" so you need to convert. Tangential velocity (v) is the linear speed of the particle ("tangent" is the direction that is perpendicular to the radius at a point on a circle).

you don't need the torque formula.
Why are you more eloquent than I am?

ok so centripetal force is $$a_c = \frac{v^2}{r}$$ and v equals the tangential speed which is 1.14 m/s, and r = .14m. So centripetal force would equal 9.345 m/s^2 right? Or is that the centripetal acceleration? It seems those two terms are used interchangeably. So what is the difference between them?

So now I have this inward force, so would the friction would be in the oppositie direction of this force?

Force is related to acceleration by F=ma
The centripetal force is the force that is required to produce the centripetal acceleration.

$$F_c=ma_c = \frac{mv^2}{r}$$

Make a diagram of all the forces on the particle and figure out what the friction has to be, keeping in mind that the net force must be equal to the centripetal force required.

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Make a diagram of all the forces on the particle and figure out what the friction has to be, keeping in mind that the net force must be equal to the centripetal force required.
I'm not sure how to find all the forces on the particle. Here is what I know

The particle will have a tangential velocity
The particle will have a centripetal acceleration that is perpendicular to the tangential velocity
Then the particle will have gravity and a normal force.
I just can't get my mind around how to tie all these together to find the friction force needed.