Confusion while trying to build intuition of centripetal force

[crudux_cruo]

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then that body would not be experiencing uniform circular motion. Therefore, the body must be experiencing a net force in the direction of the centripetal acceleration. Would a body tangentially accelerating experience a net centripetal acceleration as well?

Centripetal force is not the name for a specific type of force, but a generic name for the force/(sum of forces?) that are acting in the direction of that acceleration. In other words, these are forces that if removed would result in the body resuming linear motion. So at any instant if the centripetal force is removed, the body's inertia continues its linear path, with its speed being equal to the tangential velocity at the final moment of circular motion.

Using an example of a car making a turn on a level road, during every instant of the turn the car's inertia will keep its velocity tangent to the turn. The car does not continue in the direction of the tangential velocity, so the static friction must be keeping it on the circular path.

1)Is the friction static because the car doesn't move outside the circular path, and it's acting against the inertia of the car?
2)If the friction suddenly became kinetic, would that imply the car slides out of the turn and into a straight line?
3)Does the friction that is driving the car forward through this turn the same as the centripetal force?

Am I taking a simplification of a problem too literally and introducing things that don't belong? I would try to work this out myself but I'm not even sure if these are valid questions. I feel like I am taking a simple problem and being far too literal about it, but the concept of static friction acting over a distance is very confusing to me. I guess it technically doesn't? The friction is perpendicular to displacement so no work is done by it. At this point, I'm not even sure if that's correct.

Finally, I think I understand that the centrifugal 'force' is just how someone on a rotating referencing frame would explain their inertia and why they'd feel they are being 'pushed'. I came across this post and found these comments under the question.

Am I misunderstanding something? I thought centrifugal 'forces' weren't actual forces, and that the tension in the rope would be from whatever was pulling the bucket into circular motion. Or am I just misreading an attempt at irony or something?

I've been spinning my wheels, so any insight is appreciated.

 

[paradisePhysicist]

What do you mean by static friction? If the tires are sliding then the friction is not static, and the tires will still help the car turn even if they are sliding. Under normal conditions (not fast speeds), the tire won't be sliding and will have static friction, this will cause the tires to "warp" and bend causing a slip angle. On the other hand, if the wheels are made out of some other material that doesn't bend, then some portion of the wheel has to be sliding, since wheels contact patch is a rectangle yet the turn is a curve, and the car will still turn.

 

[crudux_cruo]

What do you mean by static friction? If the tires are sliding then the friction is not static, and the tires will still help the car turn even if they are sliding. Under normal conditions, the tire won't be sliding and will have static friction, this will cause the tires to "warp" and bend causing a slip angle. On the other hand, if the wheels are made out of some other material that doesn't bend, then some portion of the wheel has to be sliding, since wheels contact patch is a rectangle yet the turn is a curve, and the car will still turn.

Please dumb it down for me. Are you saying that the centripetal force during a car's turn is not caused by static friction?

 

[paradisePhysicist]

Please dumb it down for me. Are you saying that the centripetal force during a car's turn is not caused by static friction?

Personally I don't even like to use the concept of centripetal forces or centrifugal forces, I don't know if you are being required to use that by someone else, but personally I just prefer to just represent the forces as arrows in x and y direction then sum the forces if necessary.

"4. Centrifugal and Centripetal Forces These are two ways of describing the force on an object associated with its movement in an arc. Centripetal view X “In an inertial frame, the centripetal force is the applied force that makes the object move in an arc.” Centripetal force is a resultant force, not an applied force. ✓ “In an inertial frame, real applied forces have a real resultant force producing all the acceleration. The component normal to the velocity is termed the centripetal force. Arguably, it is better to avoid the term centripetal force altogether and only refer to centripetal acceleration

Source https://www.physicsforums.com/insights/frequently-made-errors-pseudo-resultant-forces/"

Lets say you have a car going north.

If you turn your front tires clockwise, that gives you a force, generated by the front tires, going east and south. It doesn't matter if the tires are sliding or not, the force will still be generated by them.

Since the back tires don't rotate (at least in cheap cars) there is no force on them whatsoever until after the turn actually is initiated.

Of course this occurs in an infinistemally small time and the math to compute the actual trajectory is probably exceedingly complicated. But in general terms the car will turn, computing the exact amount it will turn though will be difficult.

(Also when I said rotate I meant a steering rotation, there is still going to be rolling rotation. Also when I said none whatsoever, I meant there is still probably some minute amount of lateral force due to engineering defects and what not, but in an abstract scenario there is no lateral force.)

 

[PeroK]

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then that body would not be experiencing uniform circular motion. Therefore, the body must be experiencing a net force in the direction of the centripetal acceleration. Would a body tangentially accelerating experience a net centripetal acceleration as well?

Centripetal force is not the name for a specific type of force, but a generic name for the force/(sum of forces?) that are acting in the direction of that acceleration. In other words, these are forces that if removed would result in the body resuming linear motion. So at any instant if the centripetal force is removed, the body's inertia continues its linear path, with its speed being equal to the tangential velocity at the final moment of circular motion.

Using an example of a car making a turn on a level road, during every instant of the turn the car's inertia will keep its velocity tangent to the turn. The car does not continue in the direction of the tangential velocity, so the static friction must be keeping it on the circular path.

1)Is the friction static because the car doesn't move outside the circular path, and it's acting against the inertia of the car?
2)If the friction suddenly became kinetic, would that imply the car slides out of the turn and into a straight line?
3)Does the friction that is driving the car forward through this turn the same as the centripetal force?

Am I taking a simplification of a problem too literally and introducing things that don't belong? I would try to work this out myself but I'm not even sure if these are valid questions. I feel like I am taking a simple problem and being far too literal about it, but the concept of static friction acting over a distance is very confusing to me. I guess it technically doesn't? The friction is perpendicular to displacement so no work is done by it. At this point, I'm not even sure if that's correct.

Finally, I think I understand that the centrifugal 'force' is just how someone on a rotating referencing frame would explain their inertia and why they'd feel they are being 'pushed'. I came across this post and found these comments under the question.

Am I misunderstanding something? I thought centrifugal 'forces' weren't actual forces, and that the tension in the rope would be from whatever was pulling the bucket into circular motion. Or am I just misreading an attempt at irony or something?

I've been spinning my wheels, so any insight is appreciated.

First, you are over-complicating this. We have Newton's second law: $\vec F = m\vec a$. That means that whatever acceleration you observe, there must be a net force in that direction. And, whatever net force you apply there will be acceleration in that direction.

For uniform circular motion, there is only net force/accleration in the centripetal direction (towards the centre). For accelerated circular motion, there must be an additional component of force in the tangential direction. More generally, for arbitrary motion, there are components of force/acceleration tangential to and orthogonal to the instantaneous velocity.

The acceleration (or deceleration) of a car is generally achieved by static friction between the tires and the road. Obviously, there are gravity and air resistance as well. If the car skids, then that is kinetic friction, which is not so efficient and leaves rubber on the road.

For a car turning normally, the centripetal force must come from static friction with the road. But, on a banked track there is also the angled normal force from the track, as a reaction to the weight of the car.

Centrifugal force is usually the opposite of centripetal and is the fictitious/inertial force that arises in an accelerating (rotating) reference frame.

 

[crudux_cruo]

Thank you all. This post is embarrassing and I understand less about the situation than I initially did, so I apologize. I'm not sure where the disconnect is happening so I can't ask for any more help than I already have, but I appreciate the effort nonetheless and will continue to work through it alone.

 

[sophiecentaur]

All I can say is why does it have to be static friction? You can only have static friction if there is no relative radial motion involved.
The wheel has to be at an angle relative to the tangent. The geometry tells us that some of the footprint must be slipping so there has to be some sliding friction.
but why be upset that a particular term doesn’t apply? There’s a force there to do the job.

 

[crudux_cruo]

All I can say is why does it have to be static friction? You can only have static friction if there is no relative radial motion involved.
The wheel has to be at an angle relative to the tangent. The geometry tells us that some of the footprint must be slipping so there has to be some sliding friction.
but why be upset that a particular term doesn’t apply? There’s a force there to do the job.

Unfortunately it would seem that my inability to communicate and my horrendous attempt at packaging several of my problems into one question has been my undoing here.

The question in the image uses static friction, and I have found other explanations using static friction as well. I have asked for an answer that is more technical than I am clearly capable of learning from, and it has obfuscated my goal here.

Again, I appreciate the response but this post was a mistake and I feel bad for wasting the effort. If the relevant people want to lock this thread, that would be great. I have not effectively communicated my misunderstandings and I am genuinely sorry.

 

[paradisePhysicist]

Thank you all. This post is embarrassing and I understand less about the situation than I initially did, so I apologize. I'm not sure where the disconnect is happening so I can't ask for any more help than I already have, but I appreciate the effort nonetheless and will continue to work through it alone.

Helps if u just view a tire as 1 component instead of studying the whole car.

Just like go to your backyard get a tire. Or just get a lego tire. The tire will resist sideways motion. So if the tire is at angle (lets say the angle is 1:00 or 2:00 clockwise). Its going to exert a force south east. This will result in a trajectory of north east.

Now attach that tire to the car, and use that as the front tire, and then add a motor to the back tires of the car.
The motor pushing the back tires is basically the same as the yoga ball.
This means the car will push the front tire the same concept as the yoga ball pushing the tire. This means the car will get an east pushing torque from the front tire, thus will rotate.

Another way to think of it is like this. Friction always offers a force opposite of motion. A tire has a heavy side friction and the longitude friction is the rolling resistance. So even if the car is sliding, there will in most cases be more side friction than longitudal friction.Another example is if brakes are applied (no ABS.) The tire will not be able to spin. Therefore the friction will just behave like a normal object roughly equal in both directions. Therefore the car will not turn, hence they invented ABS (antilock brakes.)

 

[crudux_cruo]

I spent some time working through some problems and rereading this thread, and hopefully that did some good.

I drew this chickenscratch really quickly and was curious if you felt that it was roughly accurate? I only did the forces for one of the front tires for simplicity, and I'm having a bit of trouble conceptualizing the entire car as a system but hopefully I'm closer than where I started out.

 

[paradisePhysicist]

I spent some time working through some problems and rereading this thread, and hopefully that did some good.

I drew this chickenscratch really quickly and was curious if you felt that it was roughly accurate? I only did the forces for one of the front tires for simplicity, and I'm having a bit of trouble conceptualizing the entire car as a system but hopefully I'm closer than where I started out.

Hmm, I am not sure what these letters are.

https://www.physicsforums.com/attachments/screen-shot-2021-07-11-at-10-04-15-png.285786/
That is not a realistic question, the answer would depend on a lot of factors, like suspension, tire flexibility, length and width of the car, etc., irl there are tire curves, they don't just function like a binary sliding or static friction.

I think what they are actually trying to ask is if you have a cardboard box (like an amazon package) and are moving it around a turn, what speed until the friction turns into sliding friction.

First you need to calculate what is the maximum force the box can take before sliding.

you can use force of friction = (coefficient of friction)(normal force) and just set the nf to 9.8, mass can just be normalized to 1.

There may be a more optimized way to do this than that method, because with that method you will then need to convert lateral acceleration into lateral velocity, but this is what I got so far.

 

[crudux_cruo]

The question is as realistic as any of the questions I am being asked at my level, so I'm okay with the understanding I think I have. For now cars are just boxes with friction, hopefully one day I'll be able to work with further complexity.

I appreciate the time and patience you spent on this exchange with me, and I think I can say I know more than when I first made this post.

 

[sophiecentaur]

I think what they are actually trying to ask is if you have a cardboard box (like an amazon package) and are moving it around a turn, what speed until the friction turns into sliding friction.

That's a much better question and one we could all have a valid stab at answering!

 

[PeterO]

If you used a Golf Cart to study the concept, think as follows.
If you removed on the the wheels from the cart, with its stub axle, you could push it along parallel to the tyre, and it would roll easily.
If you arranged the tyre to be sideways to motion, you could push and achieve very little motion - the lateral resistance that can be produced between the tyre and the surface would balance the force you were applying.
There is a chance that if you pushed hard enough, the tyre would start to slide sideways. That slipping resistance force would be less than the maximum friction before the tyre slipped.
With the wheels back on the Golf Cart, you could begin driving straight ahead.
You then turn the wheels (angle them slightly to the direction of travel). Angling the tyres will generate an amount of lateral friction on the tyre (not as much as when you pushed the tyre sideways.
That force will try to deflect the cart, and slow the cart down. (by pressing the accelerator, you might be able to prevent the cart reducing its speed, but the deflection force, at right angles to the motion, amount to a centripetal force.
analysis of the circular motion will show what radius of circle will be achieved with each particular deflection force.
If you wish to drive around a circular track, that radius has to match the radius of the track.
If you were to increase your speed, the deflection force has to get bigger (to maintain the same radius)
If you attempt to drive too fast, you will reach the point when the lateral friction cannot be achieved, the tyre starts to slide across the surface and the lateral friction reduces markedly (you begin to skid)
With the now reduced centripetal force, the radius of your circle increases - and no longer matches the radius of the track.

A circular track, say 3m wide, might have an inner radius of 20m, and an outer radius of 23m.
If the turning force generated enables you to maintain a circle of radius 20m, you can drive your car around touching the inside edge of the track.
If the turning force enables you to maintain a circle of radius of 23 m, you can drive around touching the outer edge of the track.
If the turning force only enables you to maintain a radius of 30m, then your circular path, overlaid on the track, may start with your wheels on the inner edge of the track, but you will move further and further from that edge. AT some point you will move beyond the outer edge of the track.
Most drivers describe that situation as "I drove too fast and spun out!"

 

[PeterO]

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then that body would not be experiencing uniform circular motion. Therefore, the body must be experiencing a net force in the direction of the centripetal acceleration. Would a body tangentially accelerating experience a net centripetal acceleration as well?

Using an example of a car making a turn on a level road, during every instant of the turn the car's inertia will keep its velocity tangent to the turn. The car does not continue in the direction of the tangential velocity, so the static friction must be keeping it on the circular path.

1)Is the friction static because the car doesn't move outside the circular path, and it's acting against the inertia of the car?

The friction is static, because the tyres are not slipping on the surface - the brakes are not locked on, the wheels are not spinning under attempted acceleration and the tyres are not slipping across the surface, but rolling in a direction along their circumference

2)If the friction suddenly became kinetic, would that imply the car slides out of the turn and into a straight line?

The friction suddenly becoming kinetic means the tyres are now sliding (to some extent) across the surface.
If the sliding is due to the brakes suddenly being locked on, then the car may well now slide in a straight line. If the sliding is simply due to (attempting t) exceeded the lateral grip the tyre could supply, the deflecting force may merely be reduced, but not to zero. In that case the car will continue to travel in a circular path, but one of greater radius that the curve in the road. You can check the effect of that by drawing circles using a compass and pencil.
Using a common centre draw one circle, and one larger circle - you will then have a model of the track you were trying to follow.
Now open the compass further, but place the pencil on the inner circle - and therefore the point further away than you original two circles.
Now draw the circle, and you will notice the path gets further and further from the inside of the bend, eventually reaching the outside of the bend. Keep going and you will find the path "off into the paddocks" that the car may take. Indeed once leaving the road, the friction will drop even more (on the grass) and may well approximate a straight line from there.

3)Does the friction that is driving the car forward through this turn the same as the centripetal force?

Not sure what you mean by "driving the car forward through the turn". If you mean the force required to maintain the "forward" motion (eg drive around a corner at a constant 30 miles per hour / 48 km per hour then that force will be provided via the driven wheels of the car.

If you mean does the friction - mostly lateral - "drive" the car around the corner (cause it to turn) then yes it is the centripetal force - however the total centripetal force is a complicated sum of the forces on all four wheels of a real car.

Finally, I think I understand that the centrifugal 'force' is just how someone on a rotating referencing frame would explain their inertia and why they'd feel they are being 'pushed'. I came across this post and found these comments under the question.

Centrifugal 'force" is an imaginary force, which our minds invent to explain what is happening in an accelerated frame of reference. We spend 99.9% of our lives in a frame of reference which is not accelerating.
Imagine you were invited to the front of the room to write something on the board.
You begin at rest, beside your seat. You then briefly accelerate to a velocity of 1m/s towards the board (you start walking). You maintain that constant velocity for a few seconds, then reach the board. You accelerate (decelerate if you must) briefly reducing your velocity to 0 m/s (you stop at the board). You spend some time there writing on the board. You then accelerate briefly (start walking back to your seat), travel at constant velocity for a few seconds, the briefly accelerate to 0 m/s again (you stop at your seat) then sit down.
During that whole process, you spent less than 1 second of the occurrence accelerating. Such a small time, that you never considered how those brief acceleration were achieved.

If you were a passenger in a Ferrari, which was accelerating at the greatest rate the driver could achieve, you will notice a length period of time during which the seat of the car is pushing strongly (forward) on you. You have time to contemplate "why is this seat pushing me?". If the car was parked (stopped accelerating) the only way to have the seat push you like that would be for something/someone to literally push you into the seat - with the seat then providing the reaction force to balance.
Grasping at straws we are likely to say something like "wow - that car really pushed me into the seat when you took off, it must have a really powerful engine".

When a car travels in a circle, it applies a centripetal Force on you. First reaction is "Wow, the car is pushing me towards the centre, there must be something pushing out, for balance (like during the other 99% of my life).

Am I misunderstanding something? I thought centrifugal 'forces' weren't actual forces, and that the tension in the rope would be from whatever was pulling the bucket into circular motion. Or am I just misreading an attempt at irony or something?

I've been spinning my wheels, so any insight is appreciated.

 

[sophiecentaur]

I still don’t get the obsession with static friction here. Not much skill needed to drift round a corner (arc of a circle) with all wheels slipping and the engine providing high enough dynamic friction force.
A small cost will get you a trial ride on a skid pan if you don’t accept what I say.
Classifying the centripetal force doesn’t get you anywhere in understanding this.