# Uniform motion experiment

Silverbeam
Hi, I’m new here and I signed up to ask for some help with a physics problem.

I’m not trained, nor am I receiving training, in physics. I’m a bachelor of Geoscience student halfway through my course.

The problem I have is with understanding and testing the law of uniform motion (I think that’s the right thing to call it). I know someone who is extremely sceptical of gravity and orbital mechanics. Yes, he is a flat earther, but a particularly intelligent one, and he disputes the concept of acceleration being required to keep a body in uniform circular motion.

To make his point he asked what a car driving around and around in a circle would do if it were accelerating. He says it must speed up.

From this argument I conceived of an experiment in which a car is driven in a series of identical circles until a constant speed is maintained but no further adjustments are made to acceleration. The car is then allowed to straighten out, without adjusting the acceleration. As the car then travels in a straight line, if an increase in speed is observed it would mean that acceleration had been applied while the car was going in the circles, even though it had a uniform speed. This concept makes sense to me, but I don’t always make sense, so if anyone sees any problems with it, please let me know so I can devise something better.

I decided to run the experiment in a carpark and the results seemed to confirm the law. I was able to maintain uniform motion in a series of circles, straightened out the car and found it sped up. I ran four trials and filmed the last one to confirm what my speedometer indicated while I was driving. When I got home, I analysed the footage, took measurements, and wrote up the results in a short preliminary report. I can provide the video or report if anyone would like to see them.

The problem arose when I shared my findings with my flat earther acquaintance. He said I had not accounted for the friction and drag on the vehicle due to the centrifugal force. He claimed this was the reason I had to apply acceleration throughout the series of circles I did in the car.

This seemed like a valid criticism, and something I had not considered. I decided to try to find out if there were some way to calculate the forces involved and what amount of the accelerating force would account for the drag experienced by the vehicle. Unfortunately, I haven’t found anything very helpful except a formula for calculating centrifugal force given mass, velocity and radius of the circle.

Can anyone help me with this?

Thank you :)

Mentor
The problem arose when I shared my findings with my flat earther acquaintance. He said I had not accounted for the friction and drag on the vehicle due to the centrifugal force.
He’s right about this. It takes more power to keep a car moving against friction when it’s turning than going in a straight line. And...
As the car then travels in a straight line, if an increase in speed is observed it would mean that acceleration had been applied while the car was going in the circles, even though it had a uniform speed.
You are wrong about this. Suppose you tie a weight to a string and swing it in a circle; that’s uniform circular movement. Now if the string breaks the weight moves off in a straight line tangent to the circle at the exact same speed. It has to: at the moment before the string breaks it’s moving in that direction at some speed; the string breaks so now there’s no force on the weight so it keeps on moving in the same direction with the same speed.

So your experiment isn’t showing what you want to show. Perhaps a simpler way of making your point would be to carry an accelerometer - you can get accelerometer apps for most smartphones - in the car while driving at a constant speed in a circle.

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• russ_watters and Dale
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The problem arose when I shared my findings with my flat earther acquaintance.

Can anyone help me with this?
No one can help. Anyone who believes in flat Earth will never accept any argument about anything. You're wasting your time. • Delta2, davenn, hutchphd and 4 others
Mentor
Summary:: Need help with calculating centrifugal drag on a turning vehicle and the force required to overcome it and maintain uniform motion.

To make his point he asked what a car driving around and around in a circle would do if it were accelerating.
Accelerometers are devices that measure proper acceleration. Simply record an accelerometer during driving around in the circle to show that there is inward acceleration.

However, he will reject this measurement. Flat earthers are immune to evidence. The accelerometer reading will be helpful for you, but not for him.

• davenn and sophiecentaur
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Flat earthers are immune to evidence.
... otherwise, they wouldn't be flat-Earthers in the first place!

One interesting corollary is that it implies a centuries-old global conspiracy, currently involving not only the Western World, but the Chinese, Russians, Indians and the Muslim World. Which has remained unshakeable through world wars, the cold war and modern global conflicts. No one, apparently, wants to gain the huge scientific, commercial and military advantages associated with admitting that the Earth is flat! And, adopting the replacement for mainstream modern science that this implies.

• Dale
DrStupid
Accelerometers are devices that measure proper acceleration. Simply record an accelerometer during driving around in the circle to show that there is inward acceleration.

That works for the car but not for "gravity and orbital mechanics". An accelerometer in the ISS shows almost nothing even though it is accelerated in classical physics (in contrast to general relativity).

Why not just doing the math? Acceleration is the second time derivate of the position. Calculate that for circular motion and you have the centripetal acceleration. That is hard to dispute - even for flat-Earthers.

• Dale
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That is hard to dispute - even for flat-Earthers.
Well, you have more confidence in their persuadability than I do. But you are right, the coordinate acceleration may be more useful than the proper acceleration. We can hardly expect flat earthers to understand a geometric theory like general relativity when they struggle with geometry.

• davenn, Klystron and PeroK
Silverbeam
You are wrong about this. Suppose you tie a weight to a string and swing it in a circle; that’s uniform circular movement. Now if the string breaks the weight moves off in a straight line tangent to the circle at the exact same speed. It has to: at the moment before the string breaks it’s moving in that direction at some speed; the string breaks so now there’s no force on the weight so it keeps on moving in the same direction with the same speed.

I don’t see how your example relates to my experiment. A weight on a string gets its inward acceleration from whatever is swinging it around. If the string breaks, it is cut off from the source of that acceleration, so I imagine it would do as you say and continue at a tangent with the same speed it had while circling. In my experiment the object in motion is never cut off from the source of its inward acceleration, as the force is coming from within it, and no adjustments are made to the acceleration level when the path is changed from circular to straight, so that whatever inward force was going into the change in direction now goes into a change in forward speed. The car shows an immediate increase in speed of 36% over a distance half that of the preceding circular motion, so the outcome of removing the change in direction is much different to the outcome of simply cutting the source of inward acceleration as in your example.

If my experiment is not showing what I want it to show, what is it showing when I observe the car increasing in speed along the straight compared to the circle, when no change has been made to accelerative force?

Silverbeam
I’m not testing the law of uniform motion because I think I can change my friend’s mind on gravity or the Earth’s shape. I know several flat earthers and they are generally not interested in the truth of things and, as some have said here, will simply ignore evidence that falsifies their ‘model’ or expand the conspiracy to account for the anomaly. Its more for my own satisfaction, so that if I am arguing in favour of a gravitational force and orbital mechanics, I can know that I have found my own experimental support for what it is I am defending.

Silverbeam
Acceleration is the second time derivate of the position. Calculate that for circular motion and you have the centripetal acceleration.

Could you explain what you mean by this? As I say, I have no training in physics, so I don’t understand what you mean.

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If my experiment is not showing what I want it to show, what is it showing when I observe the car increasing in speed along the straight compared to the circle, when no change has been made to accelerative force?
The car's acceleration comes from where it always comes from: friction between the tyres and the road (*). You don't need an engine to continue in circular motion at uniform speed - although slowly the energy will disspiate through air resistance etc.

(*) If your car is in mid air and you press the accelerator, or hit the brakes, then nothing much happens. The brakes and accelerator work by inducing the appropriate friction on the road, that produces the external accelerating force.

Silverbeam
The car's acceleration comes from where it always comes from: friction between the tyres and the road. You don't need an engine to continue in circular motion at uniform speed - although slowly the energy will disspiate through air resistance etc.

Yes, friction between the tyres and the road is the interface through which the energy is transferred but the energy does not come from the tyres contacting the road, it comes from an engine causing the tyres to revolve while being in contact with the road.

A car going in circles without any energy from the engine being applied to the wheels will not continue in uniform motion as it will immediately begin slowing down, which is not uniform motion.

My experiment is to drive a car in a series of identical circles, adjusting the acceleration level until a constant speed is achieved over an identical distance for each circle. The steering is then adjusted, without adjusting the acceleration, so that the change in direction is removed while acceleration remains constant. The speed of the car is observed to increase after going straight compared to when going in circles, even though the same amount of energy is being transferred to the wheels in both situations.

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If my experiment is not showing what I want it to show, what is it showing when I observe the car increasing in speed along the straight compared to the circle, when no change has been made to accelerative force?
The frictional force has changed. You are no longer having to twist your back tires slightly (the outer edge is no longer following a slightly wider circle than the inner edge of each one), and the weight distribution of your car across the tires has changed, which probably affects rolling resistance. So you pick up speed slightly as you release the steering, not because the power input has changed but because the power dissipated has changed.

This is a common problem with trying to establish simple laws using very complex pieces of machinery. There's more going on than you might think, and effects you didn't think o can mislead you.
Could you explain what you mean by this? As I say, I have no training in physics, so I don’t understand what you mean.
If you know enough calculus to be able to differentiate a ##\sin## or ##\cos##, then it takes about three lines to prove that an object moving in a circle at constant speed has an acceleration that is pointed at the center of the circle regardless of why it's moving in a circle. If you don't know any calculus, that doesn't help you.

Silverbeam
If you know enough calculus to be able to differentiate a ##\sin## or ##\cos##, then it takes about three lines to prove that an object moving in a circle at constant speed has an acceleration that is pointed at the center of the circle regardless of why it's moving in a circle. If you don't know any calculus, that doesn't help you.

I don't know any calculus so not, that doesn't help. Is there a way of calculating the amount of friction in each phase of the experiment (the amount when circling and amount when going straight) and the amount of force required to overcome it in both phases, so that I can show that the car is undergoing more acceleration than is required to simply overcome the friction in the circling phase to maintain the uniform motion?

Mentor
That works for the car but not for "gravity and orbital mechanics". An accelerometer in the ISS shows almost nothing even though it is accelerated in classical physics (in contrast to general relativity).
No, it does work for both the car and the ISS. The phone has a 3-axis accelerometer, and the acceleration measured when stationary on the surface of the Earth is 1.0g vertically. The acceleration from the car turning is measured separately, in a perpendicular axis. For the ISS, the two accelerations are aligned and subtract to zero.

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A car going in circles without any energy from the engine being applied to the wheels will not continue in uniform motion as it will immediately begin slowing down, which is not uniform motion.
It may not slow down significantly. It doesn't take any energy to move with constant speed in a circle (any more than moving with constant speed in a straight line). The only loss of speed is through dissipation of energy (although that dissipation for practical mechanical reasons may be greater for circular motion).

Therefore, it takes no energy to accelerate in a direction perpendicular to the direction of motion. Think of a ball on a roulette wheel, once it's started it will whizz round and round, with significant centripetal acceleration, but without input of energy and only gradually lose speed.

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My experiment is to drive a car in a series of identical circles, adjusting the acceleration level until a constant speed is achieved over an identical distance for each circle. The steering is then adjusted, without adjusting the acceleration, so that the change in direction is removed while acceleration remains constant. The speed of the car is observed to increase after going straight compared to when going in circles, even though the same amount of energy is being transferred to the wheels in both situations.
This analysis is based on a fundamental lack of understanding of basic kinematic principles.

Silverbeam
This analysis is based on a fundamental lack of understanding of basic kinematic principles.
Which kinematic principles have I misunderstood and how have I misunderstood them?

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Which kinematic principles have I misunderstood and how have I misunderstood them?
$$\frac{dE}{dt} = \vec F \cdot \vec v$$
In short, uniform circular motion requires no energy input - no more than uniform linear motion. This is why the Earth can, indeed, orbit the Sun practically indefinitely without an engine!

PS where ##E## is kinetic energy.

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My experiment is to drive a car in a series of identical circles, adjusting the acceleration level until a constant speed is achieved over an identical distance for each circle. The steering is then adjusted, without adjusting the acceleration, so that the change in direction is removed while acceleration remains constant. The speed of the car is observed to increase after going straight compared to when going in circles, even though the same amount of energy is being transferred to the wheels in both situations.
To be more precise, your assumption that it takes energy to move uniformly in a circle but not a straight line is false.

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The energy is going into the steering pump hydraulics, and increased friction on the tire contact patches as they are twisted during a turn. Can't do much about the pump, but you can A/B between under and over-inflation of the tires. Do remember to return the pressure to normal before driving away, of course.

The biggest obstacle though is probably the feeling that - since you feel an acceleration - energy is being borrowed. Reasonable, but wrong.

• Delta2 and PeroK
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Yes, he is a flat earther, but a particularly intelligent one,

haha the words flatearther and intelligent are a contradiction, one denies the possibility of the other

Silverbeam
To be more precise, your assumption that it takes energy to move uniformly in a circle but not a straight line is false.
I think you have misunderstood me. I’m not assuming energy input is required for uniform circular motion, I’m trying to test the law that states an object in uniform circular motion is undergoing acceleration towards the centre of the circle. I am just referring to energy because that is where I am getting my acceleration from when I test it in my car.

Never mind the energy, I am talking about the acceleration an object is experiencing towards the centre of the circle if it moves around it at a constant speed. It is not really the force that provides the acceleration I am concerned with, whether it be gravity or a car engine, only the actual rate of acceleration experienced by the object in question depending on whether it is turning or going straight.

Authorities hold that a car needs to accelerate to turn a corner while maintaining a constant speed. If this is true then if you approach a roundabout, do a 360 circle around it, and come out going in the same direction and continue straight, all the while maintaining constant speed, then you would have to have added additional inward acceleration while making the circle, compared to when going straight on the approach and exit.

It should also be true that if you applied this extra acceleration when entering the roundabout to maintain constant speed while circling, but did not readjust your acceleration on exit, but kept it the same, your car should speed up following the exit from the roundabout.

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I think you have misunderstood me. I’m not assuming energy input is required for uniform circular motion, I’m trying to test the law that states an object in uniform circular motion is undergoing acceleration towards the centre of the circle. I am just referring to energy because that is where I am getting my acceleration from when I test it in my car.

Never mind the energy, I am talking about the acceleration an object is experiencing towards the centre of the circle if it moves around it at a constant speed. It is not really the force that provides the acceleration I am concerned with, whether it be gravity or a car engine, only the actual rate of acceleration experienced by the object in question depending on whether it is turning or going straight.

Authorities hold that a car needs to accelerate to turn a corner while maintaining a constant speed. If this is true then if you approach a roundabout, do a 360 circle around it, and come out going in the same direction and continue straight, all the while maintaining constant speed, then you would have to have added additional inward acceleration while making the circle, compared to when going straight on the approach and exit.

It should also be true that if you applied this extra acceleration when entering the roundabout to maintain constant speed while circling, but did not readjust your acceleration on exit, but kept it the same, your car should speed up following the exit from the roundabout.
You don't need energy for centripetal acceleration. Explicitly because there is no change in speed. That's your fundamental misunderstanding. Acceleration does not imply energy input.

If it did, then of course the planetary orbits would be impossible. I think you've been overly influenced by your flat-Earth friend.

For practical, mechanical reasons a car will have some dissipation of energy going in a straight line and/or turning a circle. But, that is not a kinematic reason. That's just dissipation of mechanical energy in terrestrial systems.

• davenn
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I’m trying to test the law that states an object in uniform circular motion is undergoing acceleration towards the centre of the circle.
That has nothing to do with your proposed experiment.

Here are two experiments that actually test your question:

1) get an app that let's you read the accelerometer on your smart phone, drive in a straight line at constant speed, record the acceleration vector, drive in a circle at the same constant speed, record the acceleration vector. Subtract the two vectors, the difference is your centripetal acceleration and will be towards the center.

2) record a video of something spinning with as high a temporal resolution as you can. Determine the position on three successive frames. The difference in position between the first and second frame is the first velocity. The difference in position between the second and third frame is the second velocity. The difference between the first velocity and the second velocity is the acceleration. It will be towards the center.

Silverbeam
You don't need energy for centripetal acceleration. Explicitly because there is no change in speed. That's your fundamental misunderstanding. Acceleration does not imply energy input.

If it did, then of course the planetary orbits would be impossible. I think you've been overly influenced by your flat-Earth friend.

For practical, mechanical reasons a car will have some dissipation of energy going in a straight line and/or turning a circle. But, that is not a kinematic reason. That's just dissipation of mechanical energy in terrestrial systems.
Ok, I might be close to understanding you, so let me ask this: say I’m traveling in a rocket through space at a constant speed, no friction. If I want to make a circle and exit it at the same point I entered it but lose no speed, do I need to apply my engines to supply the acceleration towards the centre of the circle in order to maintain a constant speed throughout both the straight approach and the circular motion?

Silverbeam
That has nothing to do with your proposed experiment.

Here are two experiments that actually test your question:

1) get an app that let's you read the accelerometer on your smart phone, drive in a straight line at constant speed, record the acceleration vector, drive in a circle at the same constant speed, record the acceleration vector. Subtract the two vectors, the difference is your centripetal acceleration and will be towards the center.

2) record a video of something spinning with as high a temporal resolution as you can. Determine the position on three successive frames. The difference in position between the first and second frame is the first velocity. The difference in position between the second and third frame is the second velocity. The difference between the first velocity and the second velocity is the acceleration. It will be towards the center.
I have downloaded an accelerometer app and will attempt the first experiment later today.

I don't quite understand the second one. If the object is in uniform motion, wouldn't there be no difference between the first and second velocities?

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Ok, I might be close to understanding you, so let me ask this: say I’m traveling in a rocket through space at a constant speed, no friction. If I want to make a circle and exit it at the same point I entered it but lose no speed, do I need to apply my engines to supply the acceleration towards the centre of the circle in order to maintain a constant speed throughout both the straight approach and the circular motion?
I assume you mean make a 180 degree semi-circular turn.

If you are in space there is essentially no easy way to accelerate, other than to use the gravity of nearby stars or planets. Kinematically, you need no input of energy, but the problem you have is how to produce the required force.

This is one reason why travel to Mars would be so slow: because acceleration outside the Earth's atmosphere, where there is nothing to get a grip of, is practically very difficult. It's ironic that where there is no friction to slow you down, there is also no friction to speed up, slow down or make a turn.

Silverbeam
So a force needs to be produced to turn in space at a constant speed? To get that inward acceleration?

Mentor
I don't quite understand the second one. If the object is in uniform motion, wouldn't there be no difference between the first and second velocities?
It is not in uniform motion, it is in uniform circular motion. Those are different. The first and second velocities will be different.

Silverbeam
It is not in uniform motion, it is in uniform circular motion. Those are different. The first and second velocities will be different.
Wouldn't that mean it is speeding up though? Covering more distance in less time?

• PeroK
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Wouldn't that mean it is speeding up though? Covering more distance in less time?
No. It is turning. Do you understand the difference between speed and velocity? Perhaps that is the problem.

• Delta2
DrStupid
Could you explain what you mean by this?

The position of an object in uniform circular motion is

##r = r_0 + R \cdot \left( {\begin{array}{*{20}c}
{\cos \left( {\varphi _0 + \omega \cdot t} \right)} \\
{\sin \left( {\varphi _0 + \omega \cdot t} \right)} \\
\end{array}} \right)##

the velocity is

##\dot r = \omega \cdot R \cdot \left( {\begin{array}{*{20}c}
{ - \sin \left( {\varphi _0 + \omega \cdot t} \right)} \\
{\cos \left( {\varphi _0 + \omega \cdot t} \right)} \\
\end{array}} \right)##

and the acceleration

##\ddot r = \omega ^2 \cdot R \cdot \left( {\begin{array}{*{20}c}
{ - \cos \left( {\varphi _0 + \omega \cdot t} \right)} \\
{ - \sin \left( {\varphi _0 + \omega \cdot t} \right)} \\
\end{array}} \right)##

• Delta2
Silverbeam
No. It is turning. Do you understand the difference between speed and velocity? Perhaps that is the problem.
Perhaps. I thought an object in uniform circular motion went at a constant speed, so that it would always take the same amount of time to travel indentical portions of the circle.

Mentor
Perhaps. I thought an object in uniform circular motion went at a constant speed, so that it would always take the same amount of time to travel indentical portions of the circle.
That is correct. It goes at a constant speed. Now, what about the velocity, is that constant?