Why does the mud fly off tangentially from a rotating plate?

[PhysicStud01]

Homework Statement

Homework Equations

centripetal force F = mrw^2

The Attempt at a Solution

the answer says that it is the one at the edge because F is greater since r is greater.

but should the force be inwards, why would the mud leave the plate. what force acts on it. can someone help

 

[Doc Al]

but should the force be inwards, why would the mud leave the plate. what force acts on it. can someone help

Think in terms of what holds a piece of mud onto the plate as it starts to spin. Let's call that force "mud sticky force".

Which location--edge or center--requires more "mud sticky force" as the plate starts to spin? Sooner or later, the existing "mud sticky force" will not be enough to keep the piece of mud stuck. Where will that limit be reached first?

 

[PhysicStud01]

Think in terms of what holds a piece of mud onto the plate as it starts to spin. Let's call that force "mud sticky force".

Which location--edge or center--requires more "mud sticky force" as the plate starts to spin? Sooner or later, the existing "mud sticky force" will not be enough to keep the piece of mud stuck. Where will that limit be reached first?

is it the contact force? but this is vertical while the centripetal is horizontal.

you won't affect each other, right?

+ won't the contact forces be equal whether at the edge or center as the weight is constant?could you be a bit clearer
thanks

 

[Doc Al]

is it the contact force? but this is vertical while the centripetal is horizontal.

Think of there being a force preventing a piece of mud from sliding around, analogous to friction. The force will be horizontal. But it is not infinitely strong--sooner or later it won't be enough to hold the mud in place.

 

[PhysicStud01]

Think of there being a force preventing a piece of mud from sliding around, analogous to friction. The force will be horizontal. But it is not infinitely strong--sooner or later it won't be enough to hold the mud in place.

could you tell me which force in physics this actually is. (i know this is not aksed in the question, but i want to properly understand what is happening)

and why does the mud not have a centripetal force on it - it's moving in circular motion too.

 

[Doc Al]

could you tell me which force in physics this actually is. (i know this is not aksed in the question, but i want to properly understand what is happening)

Don't get hung up on the details of this force. At the root, it will be an electromagnetic force. (So is friction.) The main idea is that something must be exerting a horizontal force on the mud so it can move in a circle.

and why does the mud not have a centripetal force on it - it's moving in circular motion too.

Don't think of "centripetal force" as a separate force; it's just a generic name. The actual force creating the centripetal acceleration is the horizontal force that we are talking about. The "mud force" is the centripetal force!

 

[PhysicStud01]

Don't get hung up on the details of this force. At the root, it will be an electromagnetic force. (So is friction.) The main idea is that something must be exerting a horizontal force on the mud so it can move in a circle.Don't think of "centripetal force" as a separate force; it's just a generic name. The actual force creating the centripetal acceleration is the horizontal force that we are talking about. The "mud force" is the centripetal force!

Electromagnetic??

i would not even think of this. should there be charges / electricity or magnets to have an electromagnetic force?

by the way, would the mud get thrown in the same direction of rotation of the disc, or the inverse or tangential?
thanks

 

[Doc Al]

Electromagnetic??

i would not even think of this. should there be charges / electricity or magnets to have an electromagnetic force?

Lots of composite forces are primarily electromagnetic. (Realize that atoms and molecules are made of charged particles.) For example: The force that the ground exerts on you when you stand (the normal reaction force) is also primarily electromagnetic.

by the way, would the mud get thrown in the same direction of rotation of the disc, or the inverse or tangential?

Consider Newton's 1st law. The mud "wants" to keep going straight, but the sticky forces from the table are preventing that, forcing it to move in a circle along with the rotating plate. Up to a point.

 

[haruspex]

but should the force be inwards, why would the mud leave the plate.

Centripetal force is not an applied force. If a body is moving in an arc, there must be a force acting on it to achieve that. If you add up all the forces acting on the body, and take the component of that which is orthogonal to the current velocity, that is the centripetal force.
A body with no forces acting on it moves in a straight line at constant speed. If no horizontal forces act on the mud it will move in a straight line off the edge of the plate.
In order for the mud to stay where it is on the rotating plate, it requires a centripetal force. The question is, where does that force come from, and will it be enough to stop the mud sliding off?

 

[PhysicStud01]

Centripetal force is not an applied force. If a body is moving in an arc, there must be a force acting on it to achieve that. If you add up all the forces acting on the body, and take the component of that which is orthogonal to the current velocity, that is the centripetal force.
A body with no forces acting on it moves in a straight line at constant speed. If no horizontal forces act on the mud it will move in a straight line off the edge of the plate.
In order for the mud to stay where it is on the rotating plate, it requires a centripetal force. The question is, where does that force come from, and will it be enough to stop the mud sliding off?

but if it's friction, should not there be a relative motion between them. if both are rotating, how will there be friction?

+ I'm still in doubt why it's not the contact force that keeps if on the disc. is this not the case for other situations?

 

[Doc Al]

but if it's friction, should not there be a relative motion between them. if both are rotating, how will there be friction?

What about static friction? Relative motion is not required.

+ I'm still in doubt why it's not the contact force that keeps if on the disc. is this not the case for other situations?

What do you mean by "contact" force? Friction is a contact force.

 

[PhysicStud01]

What about static friction? Relative motion is not required. What do you mean by "contact" force? Friction is a contact force.

sorry, i mean the normal reaction due to weight.

about the static friction. the mud would get thrown off instantly, won't it. because it's constant. but u don't think this would happen in a real case. + the question asks which will go first?

 

[jbriggs444]

sorry, i mean the normal reaction due to weight.

about the static friction. the mud would get thrown off instantly, won't it. because it's constant. but u don't think this would happen in a real case. + the question asks which will go first?

Suppose that instead of a circular plate that is rotated you have a square plate that is tilted. Will the mud all slide off the instant that the plate is tilted by a fraction of a degree?

 

[PhysicStud01]

Suppose that instead of a circular plate that is rotated you have a square plate that is tilted. Will the mud all slide off the instant that the plate is tilted by a fraction of a degree?

no. but the instant the component of the weight is greater, the mud would move off immediately, right.

+ the firction would oppose the motion, but in the above case, from what i read from the others, it seems that it is the friction that causes it to move off?

could you explain

 

[jbriggs444]

no. but the instant the component of the weight is greater, the mud would move off immediately, right.

Right. The instant the component of weight that is tangent to the surface exceeds static friction, the mud would slide off. That is the mud-behavior that the problem assumes.

+ the firction would oppose the motion, but in the above case, from what i read from the others, it seems that it is the friction that causes it to move off?

The others are not saying that static friction causes it to move off. They are saying that static friction is what keeps the mud in place on the rotating plate. The problem is that "in place on the rotating plate" means "moving in a circle along with the plate". It takes centripetal force to move in a circle. That centripetal force is provided by static friction.

 

[PhysicStud01]

Right. The instant the component of weight that is tangent to the surface exceeds static friction, the mud would slide off. That is the mud-behavior that the problem assumes.The others are not saying that static friction causes it to move off. They are saying that static friction is what keeps the mud in place on the rotating plate. The problem is that "in place on the rotating plate" means "moving in a circle along with the plate". It takes centripetal force to move in a circle. That centripetal force is provided by static friction.

but then, why dose the mud move off? the centripetal / friction is greater at the edge, right?

+ in the exampe you give, the mud would move if tilted enough. but if the tilt is not change, it may remain still. now, in this case of the question above, the normal reaction is actually constnat.

could you clear this for me.

 

[jbriggs444]

but then, why dose the mud move off? the centripetal / friction is greater at the edge, right?

The centripetal force required to maintain circular motion is greater than at the edge. That is correct. The maximum force of static friction is what it is. It is constant everywhere on the plate.

The mud slides off the rotating plate if the centripetal force that is required to maintain circular motion is greater than the maximum force that static friction can supply.
The mud slides off the tilted plate if the component of gravity parallel to the plate is greater than the maximum force that static friction can supply.

+ in the exampe you give, the mud would move if tilted enough. but if the tilt is not change, it may remain still. now, in this case of the question above, the normal reaction is actually constnat.

If you stand on a rotating merry-go-round you have to lean inward to stay in position. If you stand at the center you do not have to lean in at all. If you stand farther toward the edge, do you have to lean inward at a steeper angle in order to keep your balance?

 

[haruspex]

but then, why dose the mud move off? the centripetal / friction is greater at the edge, right?

You are still thinking of centripetal force as though it is an applied force. It is the force that would be needed to keep it on the plate. If the friction is not strong enough to provide the necessary centripetal force then the mud will slide off. The required centripetal force is greatest at the greatest radius. Does the available frictional force depend on the radius?

 

[PhysicStud01]

The centripetal force required to maintain circular motion is greater than at the edge. That is correct. The maximum force of static friction is what it is. It is constant everywhere on the plate.

The mud slides off the rotating plate if the centripetal force that is required to maintain circular motion is greater than the maximum force that static friction can supply.
The mud slides off the tilted plate if the component of gravity parallel to the plate is greater than the maximum force that static friction can supply.If you stand on a rotating merry-go-round you have to lean inward to stay in position. If you stand at the center you do not have to lean in at all. If you stand farther toward the edge, do you have to lean inward at a steeper angle in order to keep your balance?

so, the firction supplies the centripetal. but if it is centripatal, the direction is towards the centre. how then does the mud move outwards

 

[PhysicStud01]

You are still thinking of centripetal force as though it is an applied force. It is the force that would be needed to keep it on the plate. If the friction is not strong enough to provide the necessary centripetal force then the mud will slide off. The required centripetal force is greatest at the greatest radius. Does the available frictional force depend on the radius?

i know. in order words, you are saying the frictional force is centripetal (acts towards the centre). but why does the mud move out if the force on it is towards the centre?

 

[haruspex]

i know. in order words, you are saying the frictional force is centripetal (acts towards the centre). but why does the mud move out if the force on it is towards the centre?

Because it is not a strong enough force towards the centre.

 

[PhysicStud01]

Because it is not a strong enough force towards the centre.

but then what is and where does the force that moves it out come from? it's confusing

 

[haruspex]

but then what is and where does the force that moves it out come from? it's confusing

It doesn't require a force to move it out. As I reminded you earlier, if there is no force acting on a moving body then it will move at constant velocity. That means, at the same speed and in the same straight line. Moving in a straight line will take it off the plate.
If there is some frictional force, but not enough, it will move in an arc, but at too great a radius compared to its position on the plate, so it will still slid off.

 

[jbriggs444]

but then what is and where does the force that moves it out come from? it's confusing

If you have learned about frames of reference then the "outward" motion is because you are adopting a rotating frame of reference rather than an inertial reference frame. But it seems unlikely that you have learned about frames of reference yet.

As viewed by someone standing on the ground and watching the plate, the mud does not slide outward. Each blob of mud flies off tangentially -- maintaining its current speed and direction. Since the mud was moving while it was on the plate, it continues moving after it has flaked off.

It flakes off when the force of friction is not sufficient to keep accelerating it in a circular path any longer.