Circular Motion Clarification-Centrifugal Force

[ThomasMagnus]

Circular Motion Clarification--Centrifugal Force

At most amusement parks, there is a ride where the floor of a rotating cylindrical room falls away, leaving the backs of the riders "plastered" against the wall.

What is causing the rider to be pushed against the wall? Is it the fictitious centrifugal force as a result of being in a non-inertial reference frame? Or could this be explained by Newton’s first law: The people tend to want to travel in a straight line, but the wall corrects this by pushing them back in.

I know that there is centripetal force acting upon them, but this acts towards the center of a circle. I am very confused by this imaginary force pushing outward.
Another one would be: Why doesn’t water fall out of a rotating bucket?

Thanks, I appreciate the help!

 

[Doc Al]

What is causing the rider to be pushed against the wall? Is it the fictitious centrifugal force as a result of being in a non-inertial reference frame?

There's no harm in thinking that, as long as you realize that the centrifugal force is just an artifact of describing things from a non-inertial frame.

Or could this be explained by Newton’s first law: The people tend to want to travel in a straight line, but the wall corrects this by pushing them back in.

Yes, that works.

I know that there is centripetal force acting upon them, but this acts towards the center of a circle.

Without that centripetal force, the person would continuing moving in a straight line.

I am very confused by this imaginary force pushing outward.

Only the centrifugal force is 'imaginary'; you do not need to view things from a non-inertial frame. From an inertial frame, something moving in a circle is centripetally accelerated and thus requires a centripetal force.

Another one would be: Why doesn’t water fall out of a rotating bucket?

It essentially the same thing. (As was your recent question about roller coasters.)

 

[ThomasMagnus]

Thank you for your quick response DocAl!

If I was describing this force pushing outward in an inertial reference frame, how would I do that? Is the only way it can be described in a non-inertial frame?

Thanks!

 

[Doc Al]

Here's another example that might help. Imagine you're on an elevator that is accelerating upwards. You feel pressed against the floor with a force greater than your normal weight. Is there some mysterious force pushing down on you (in addition to gravity)? No. The extra force is just a consequence of being accelerated by the elevator. It pushes up on you with a force greater than your weight in order to accelerate you.

It's really the same thing with circular motion, except that the centripetal acceleration may be a bit more subtle to visualize.

 

[Doc Al]

If I was describing this force pushing outward in an inertial reference frame, how would I do that?

But there really isn't a force pushing the person outward! From the usual inertial frame, there is no such outward force.

Take a look at my last post (which I posted while you were posting your last post). It may help.

 

[ThomasMagnus]

Aha!

So then this "fictitious centrifugal force" that is felt is a consequence of being in an non-inertial reference frame?

Thanks

 

[ThomasMagnus]

But there really isn't a force pushing the person outward!

I get that it is not an actual force; however, it is very hard to wrap your mind around something that you can feel, but really isn't a force.

 

[Doc Al]

Aha!

So then this "fictitious centrifugal force" that is felt is a consequence of being in an non-inertial reference frame?

Yes!

 

[ThomasMagnus]

I assume that there is a lot more known in the world of physics about motion in inertial frames than in non-inertial frames?

 

[Doc Al]

I get that it is not an actual force; however, it is very hard to wrap your mind around something that you can feel, but really isn't a force.

What you directly 'feel' is the surface pushing against you, which is quite real. That seems like you're being pushed back into the surface, but it's really the surface pushing against you, accelerating you.

Imagine this. You are in an elevator (once again) just sitting still. All of a sudden the floor drops out of the elevator. So the force of the floor pushing you up is gone, even though gravity is still acting on you. You 'feel' weightless, since your support force is gone.

It's tricky stuff!

 

[ThomasMagnus]

And it would be correct to say that Newton's first law would explain the surface pushing on you? (particularly in the roller coaster problem).

Just to confirm, Newton's first law would only be true in an inertial frame?

 

[Doc Al]

I assume that there is a lot more known in the world of physics about motion in inertial frames than in non-inertial frames?

Why would you think that? You can (with a bit of training) translate from one to the other without issue.

There are certain situations where you'd be nuts to try to describe things from an inertial frame. For example, the motion of wind along the Earth's surface. Since the Earth is rotating, it's much simpler to make use of 'fictitious forces' such as centrifugal and coriolis forces, even though these are just artifacts of being in a rotating frame of reference. It would be unnecessarily complicated (but doable) to describe such things from an inertial frame.

 

[Doc Al]

And it would be correct to say that Newton's first law would explain the surface pushing on you? (particularly in the roller coaster problem).

Newton's first law would tell you that there must be a net force pushing on you, if you're accelerating--such as when you are forced to move in a circle instead of just moving straight. Newton's 2nd law will tell you what that force is.

Just to confirm, Newton's first law would only be true in an inertial frame?

Yes. Newton's laws need to be modified for use in a non-inertial frame. (Modified by the introduction of 'fictitious' forces.)

 

[ThomasMagnus]

Why would you think that? You can (with a bit of training) translate from one to the other without issue.

There are certain situations where you'd be nuts to try to describe things from an inertial frame. For example, the motion of wind along the Earth's surface. Since the Earth is rotating, it's much simpler to make use of 'fictitious forces' such as centrifugal and coriolis forces, even though these are just artifacts of being in a rotating frame of reference. It would be unnecessarily complicated (but doable) to describe such things from an inertial frame.

If I am standing on the surface of the Earth (not moving), I am said to be in an inertial frame, correct? Are reference frames relative to an observer? Would I be in a non-inertial frame because of acceleration due to gravity?

Thanks (I'm new at this, so my questions might seem a little odd )

 

[D H]

Just to confirm, Newton's first law would only be true in an inertial frame?

Fictitious forces arise from an attempt to make Newton's first and second laws appear to be valid in a non-inertial frame. For example, consider that cylindrical rotating room you discussed in the opening post. The centripetal force that pushes a person stuck on the wall inward is present in all frames (it's a real force). From the perspective of a frame rotating with the room, that person glued to the wall is stationary. To make Newton's first law appear to apply we need a fictitious force directed outward that exactly cancels this real centripetal force. The net force is zero, so voila! Newton's first law still works.

It is Newton's third law that is only valid in an inertial frame.

 

[ThomasMagnus]

The centripetal force that pushes a person stuck on the wall inward is present in all frames (it's a real force).

Doesn't the centripetal force act radially inward? Why wouldn't they be pulled inward by that force?

 

[Doc Al]

If I am standing on the surface of the Earth (not moving), I am said to be in an inertial frame, correct?

For many purposes you can ignore the rotation of the Earth and say you are approximately in an inertial frame. (But you're really accelerating.) It depends on the application.

Are reference frames relative to an observer? Would I be in a non-inertial frame because of acceleration due to gravity?

The surface of the Earth is a non-inertial frame because it's accelerating (it's rotating). Forgetting general relativity for the moment, you'd be in a non-inertial frame because of acceleration due to gravity if you were in free fall.

 

[Doc Al]

Doesn't the centripetal force act radially inward? Why wouldn't they be pulled inward by that force?

They are! Remember, the people are being centripetally accelerated by the wall.

 

[D H]

If I am standing on the surface of the Earth (not moving), I am said to be in an inertial frame, correct?

You aren't *in* any frame. Your existence is independent of the frame that I choose to use to describe your motion.

That said, I can describe your state from the perspective of a frame fixed with respect to the Earth (a frame such that when you stand still your velocity is zero). This is not an inertial frame. It is a rotating reference frame, with a rotation rate of about one revolution per sidereal day. Because the Earth is accelerating toward the Sun and the Moon due to gravity, this is also an accelerating reference frame.

In many applications one can ignore the fictitious centrifugal, coriolis, or inertial forces that arise from this Earth-fixed frame being both a rotating and accelerating frame. You can quite accurately describe the flight of a thrown baseball without worrying about those fictitious forces. Sometimes you can't ignore those effects. For example, the coriolis force is quite important when it comes to describing the behavior of a hurricane.

 

[ThomasMagnus]

They are! Remember, the people are being centripetally accelerated by the wall.

Let me see if I can summarize what has been said:

Without the walls of the cylinder, the riders would fly out tangentially to the circle.
The wall is the source of the centripetal force on the riders, and this force acts radially inward.
The normal force applied by the wall would be equal to the centripetal force (?)

So just like that last roller coaster problem, their bodies want to move in a straight path (Newton's first law), but the walls prevent this (this is why they are "squished" against the walls)

Seem right?

Thanks!

 

[Doc Al]

Let me see if I can summarize what has been said:

Without the walls of the cylinder, the riders would fly out tangentially to the circle.
The wall is the source of the centripetal force on the riders, and this force acts radially inward.
The normal force applied by the wall would be equal to the centripetal force (?)

So just like that last roller coaster problem, their bodies want to move in a straight path (Newton's first law), but the walls prevent this (this is why they are "squished" against the walls)

Seem right?

Sounds good to me.

 

[ThomasMagnus]

Sounds good to me.

Well, Thank you very much for your help, all of you!

 

[RedX]

Well, Thank you very much for your help, all of you!

Something that once bothered me is what if you're a dancer and do a pirouette: what would be the motion of the audience? If you spin at constant angular velocity clockwise, then in your frame the audience would be spinning at the same angular velocity but counterclockwise. That means the audience should have a centripetal acceleration pointing towards you. But the centrifugal force only points outwards! So how can this be? Well I forgot about the Coriolis force. In this situation the Coriolis force on the audience points towards you, and is twice as strong as the centrifugal force, so the audience can have centripetal acceleration about you. Thought I'd share that point of confusion.

In inertial frames, objects being observed feel like they're in a zoo. In non-inertial frames, the tables are turned, and the audience are the animals in the zoo as they now have forces on them. But notice that those forces are truly fictitious (in that they can't feel them): when someone does a pirouette, the audience doesn't feel a force. And also note that in non-inertial frames even objects at rest can feel forces (even though the net force, as seen in the non-inertial frame, is zero), so that real forces cannot be fictionalized (but this is the carousel example all over again).

Very confusing stuff!

 

[rcgldr]

The wall is the source of the centripetal force on the riders, and this force acts radially inward.

Citing Newtons third law, forces only exist as equal and opposing pairs. The walls exert an inwards force onto a person, and the person exerts and equal and opposing outwards force onto the wall (a reaction force due to the centripetal acceleration caused by the wall). Both the person and the wall experience a deformation due to the compressive nature of this force pair (the amount of wall deformation is very small compared to the person's deformation).

Not sure if this was covered, but what's keeping the people from sliding down the wall is the friction:

(static coefficient of friction) x (rate of centripetal acceleration) / (rate of gravitational acceleration) > 1

Generally it's enough that you can sit "up" and still not slide down, although you'd need to be careful when relaxing to not slam your head into the wall. Standing would be dangerous.

 

[RedX]

Another thing that confused me once is that I once heard that the centrifugal force could provide a lifting force. I think I understand it now. Say you have a rope that is threaded through an elbow. The rope that leaves the elbow vertically - you hold in your hands, and the rope that leaves horizontally is attached to a ball. Then when you swing the ball in a circle in the horizontal plane like a helicopter, there is centrifugal force on the ball that pushes it outward. This must be countered by tension in the rope towards you. But since the rope is bent by the elbow, you have to provide this tension by pulling down on the rope vertically. But then the rope pulls up on you vertically. So if you're strong enough and pull down hard enough so that the ball is spinning around fast, then you could fly as the tension lifts you off the ground? But once you're off the ground then conservation of angular momentum will require that you be spinning in the opposite direction really fast, thus tangling your rope?

 

[rcgldr]

conservation of angular momentum

If this situation is idealized, (no energy losses, no friction, no drag, and the ball isn't rotating along the axis in the same direction as the rope), then angular momentum is conserved because the ball's speed should increase or decrease relative to 1/r, where r is the current radius of the circular path the ball travels, since the rope and elbow setup do not generate any torques.

When the ball's path changes, there's a small change in velocity that is radial (inwards or outwards), but since the tension is always radial, the change in velocity is affected by the radial tension, which changes the speed of the ball.

 

[RedX]

If this situation is idealized, (no energy losses, no friction, no drag, and the ball isn't rotating along the axis in the same direction as the rope), then angular momentum is conserved because the ball's speed should increase or decrease relative to 1/r, where r is the current radius of the circular path the ball travels, since the rope and elbow setup do not generate any torques.

When the ball's path changes, there's a small change in velocity that is radial (inwards or outwards), but since the tension is always radial, the change in velocity is affected by the radial tension, which changes the speed of the ball.

I think that's right. Another way to look at it is from the frame where the ball is at rest (a rotating frame). If the ball is at rest, then the centrifugal force is balanced by the tension you apply. But now you pull the ball inward even more. Then the Coriolis force kicks in, and pushes the ball in the direction of the angular velocity of the frame: [tex] F_{Corio}=-2(\vec{\omega} \times \vec{v}_{radial}) [/tex]. So if the rotating frame is rotating counterclockwise relative to an inertial frame, then the ball will now be moving counterclockwise relative to the rotating frame. Therefore in the rest frame you'd see the ball increasing its speed but still moving counterclockwise.

So that also explains why the speed increases or decreases when you just pull radially.

Anyways, this idea that the centrifugal force can be used as a flying mechanism is silly. It's basically the same as having a pulley, attaching a heavy weight at one end, and you hold the other end, and let the heavy way drop, thereby launching you into the air. Here you would attach the elbow to something (as you would attach the pulley to something), and once spinning you have to always pull down on the rope to provide the tension on the ball: if the spinning becomes too fast, then you will be launched into the air as ball wants to fly away and you are not heavy enough to keep it down, so you will be pulled up as well and launched into the air as the rope slides out of the elbow.

 

[rcgldr]

Here you would attach the elbow to something (as you would attach the pulley to something), and once spinning you have to always pull down on the rope to provide the tension on the ball: if the spinning becomes too fast, then you will be launched into the air as ball wants to fly away and you are not heavy enough to keep it down, so you will be pulled up as well and launched into the air as the rope slides out of the elbow.

The tension is relative to 1 / r³, so it will rapidly decrease as the radius increases. If there are no losses and no damping factor, it would end up oscillating, something like an ellipse. I did the math in an older thread.

post #34 in this thread:
https://www.physicsforums.com/showthread.php?p=1436456&postcount=34

So that also explains why the speed increases or decreases when you just pull radially.

You need to be careful when defining "radially". It's possible to always orient the force so it's always perpendicular to the path of a ball. One example from that same thread above was the case of a string winding (or unwinding) around a post. The path is involute of circle, and the speed of the ball (puck in that thread) remains constant. You have to take into account the torque at the post and what the post is attached to (usually the earth) in order for angular momentum to be conserved.

See post #21 and #32 in that same thread:
https://www.physicsforums.com/showthread.php?p=1433750&postcount=21