# Particle sliding off turntable - find friction

• vertex78
In summary, the particle on the turntable has a mass of 16 g and is located 0.14 m from the center of the rotating turntable. The turntable is rotating at 78 rev/min and there is no force that would be pushing the particle off the turntable. F=ma calculates that the friction has to be 9.345 m/s^2 in order to keep the particle from sliding off.
vertex78

## 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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vertex78 said:

## 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 into 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.

Chi Meson said:
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 into 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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wombat7373 said:
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.

## 1. What is the cause of the particle sliding off the turntable?

The main cause of the particle sliding off the turntable is the lack of sufficient friction between the particle and the surface of the turntable. Friction is the force that resists the motion of an object and in this case, the frictional force is not strong enough to keep the particle in place.

## 2. How can the friction between the particle and the turntable be increased?

The friction between the particle and the turntable can be increased by increasing the normal force between the two surfaces. This can be done by adding weight to the particle or by increasing the roughness of the turntable surface. Additionally, using a material with a higher coefficient of friction can also increase the frictional force.

## 3. What is the role of the coefficient of friction in this scenario?

The coefficient of friction is a measure of the frictional force between two surfaces. In this scenario, a higher coefficient of friction means a stronger frictional force, which can help prevent the particle from sliding off the turntable. The coefficient of friction depends on the materials of the particle and the turntable, as well as the roughness of their surfaces.

## 4. Is there a way to calculate the frictional force between the particle and the turntable?

Yes, the frictional force can be calculated using the formula F = μN, where F is the frictional force, μ is the coefficient of friction, and N is the normal force between the two surfaces. However, the exact value of the frictional force may vary depending on the conditions and variables involved.

## 5. How can the particle sliding off the turntable be prevented?

To prevent the particle from sliding off the turntable, the frictional force must be greater than the force pulling the particle away from the turntable, such as gravity. This can be achieved by increasing the normal force or by using materials with a higher coefficient of friction. Additionally, ensuring that the turntable surface is clean and free of any slippery substances can also help prevent the particle from sliding off.

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