# Can an object maintain uniform motion without any external force?

• Silverbeam
In summary, a Geoscience student sought help with understanding and testing the law of uniform motion. They devised an experiment involving driving a car in a series of circles and found that the car sped up when it straightened out, indicating the application of acceleration. However, their flat earther acquaintance pointed out the need to account for friction and drag on the vehicle due to centrifugal force. The student is now seeking help with calculating the forces involved and the necessary acceleration to maintain uniform motion. However, it seems unlikely that their flat earther acquaintance will accept any evidence presented to them.
Silverbeam said:
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 didnt answer Dale's Q to you

do you understand the difference between speed and velocity ?

Dale said:
No. It is turning. Do you understand the difference between speed and velocity? Perhaps that is the problem.
Sorry, I didn't answer your question. No, I don't understand the difference between speed and velocity.

jbriggs444 and davenn
russ_watters said:
For the ISS, the two accelerations are aligned and subtract to zero.

That's what I'm talking about. The ISS is accelerated in classical physics but the accelerometer shows zero. It doesn't work this way.

etotheipi
Silverbeam said:
Sorry, I didn't answer your question. No, I don't understand the diffrence between speed and velocity.
Velocity is what is called a vector. That means that it has a magnitude and a direction. You can think of it as an arrow. The magnitude is its length and its direction is the direction it points.

For velocity, the magnitude is called speed. So the speed is what is left of velocity when you remove the direction. But acceleration is a change in velocity, not a change in speed. So to determine acceleration you have to keep the direction information, not just the magnitude information. That is what is changing in uniform circular motion.

davenn
Dale said:
Velocity is what is called a vector. That means that it has a magnitude and a direction. You can think of it as an arrow. The magnitude is its length and its direction is the direction it points.

For velocity, the magnitude is called speed. So the speed is what is left of velocity when you remove the direction. But acceleration is a change in velocity, not a change in speed. So to determine acceleration you have to keep the direction information, not just the magnitude information. That is what is changing in uniform circular motion.
Ok, thanks.

russ_watters said:
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.

I don't really know what you mean by 'the two accelerations are aligned and subtract to zero' for the ISS case. When we're thinking in terms of GR and all that stuff, if we ignore the atmosphere then there's no force at all on the ISS (apart from the tidal forces, which we can ignore on the small scales), and so no proper acceleration. Rather than 'two accelerations cancelling', probably clearer to say that there was no proper acceleration in the first place.

Dale said:
Velocity is what is called a vector. That means that it has a magnitude and a direction. You can think of it as an arrow. The magnitude is its length and its direction is the direction it points.

For velocity, the magnitude is called speed. So the speed is what is left of velocity when you remove the direction. But acceleration is a change in velocity, not a change in speed. So to determine acceleration you have to keep the direction information, not just the magnitude information. That is what is changing in uniform circular motion.
So, if I want to approach a corner in my car, driving in a straight line, then take the corner, then drive straight ahead, all at a constant speed, do I need to provide any additional force to the car while taking the corner in order to maintain the constant speed throughout?

Silverbeam said:
So, if I want to approach a corner in my car, driving in a straight line, then take the corner, then drive straight ahead, all at a constant speed, do I need to provide any additional force to the car while taking the corner in order to maintain the constant speed throughout?

Friction from the road surface provides the necessary inward centripetal component of force. also of course this is an idealisation

In general when a body moves along a trajectory with radius of curvature ##\rho## at constant speed ##v##, there is acceleration of magnitude ##v^2/\rho## directed toward the instantaneous centre of curvature, which must be caused by a net force also directed toward the instantaneous centre of curvature.

(n.b. that in most general case where ##\dot{v} \neq 0##, you will obtain an additional component of acceleration ##\dot{v} \boldsymbol{e}_t## as well as the inward component ##(v^2 / \rho) \boldsymbol{e}_n##)

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etotheipi said:
friction from the road surface provides the necessary inward centripetal component of force. also of course this is an idealisation

in general when a body moves along a trajectory with radius of curvature ##\rho## at constant speed ##v##, there is acceleration of magnitude ##v^2/\rho## directed toward the instantaneous centre of curvature, which must be caused by a net force also directed toward the instantaneous centre of curvature
So, I would not need to apply any more acceleration to the vehicle while driving in identical circles at a constant speed, than the acceleration I would need to apply if I were driving in a straight line at a constant speed?

No that's not what i said at all! a body traveling in a straight line at constant speed undergoes zero acceleration. n.b. that this is consistent with the relation i wrote, because a straight line has radius of curvature ##\rightarrow \infty##.

Silverbeam said:
So, if I want to approach a corner in my car, driving in a straight line, then take the corner, then drive straight ahead, all at a constant speed, do I need to provide any additional force to the car while taking the corner in order to maintain the constant speed throughout?
For a car, yes, but for a marble on a smooth track that turns, no. The energy required for the car has to do with inefficiency, not fundamental physical principles.

PeroK
Dale said:
For a car, yes, but for a marble on a smooth track that turns, no. The energy required for the car has to do with inefficiency, not fundamental physical principles.
Ok, but for a marble on a track it has the sides of the track to keep it in a circle. What about a marble going in circles without a track? Doesn't it need some force to be applied to it, either attractive or repulsive, in order to constantly change its direction and keep it in a circle? Isn't that why gravity is invoked for orbits, to provide a force that maintains the inward acceleration to prevent the Moon or whatever from just going off in a straight line?

hmmm27 and etotheipi
Silverbeam said:
Ok, but for a marble on a track it has the sides of the track to keep it in a circle. What about a marble going in circles without a track? Doesn't it need some force to be applied to it, either attractive or repulsive, in order to constantly change its direction and keep it in a circle? Isn't that why gravity is invoked for orbits, to provide a force that maintains the inward acceleration to prevent the Moon or whatever from just going off in a straight line?

yes!

Silverbeam said:
Doesn't it need some force to be applied to it, either attractive or repulsive, in order to constantly change its direction and keep it in a circle?
Yes, it does.

I may have misunderstood your question earlier. I thought you were asking if you would need to step on the gas in a car to maintain speed through a turn. It is not necessary for a marble to “step on the gas” as it were. It needs the track, but not a push along the track, unlike a car which needs the push too.

Silverbeam said:
Isn't that why gravity is invoked for orbits, to provide a force that maintains the inward acceleration to prevent the Moon or whatever from just going off in a straight line?
Yes.

etotheipi said:
yes!
But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?

Dale said:
I may have misunderstood your question earlier. I thought you were asking if you would need to step on the gas in a car to maintain speed through a turn. It is not necessary for a marble to “step on the gas” as it were.
That is what I meant.

Silverbeam said:
But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?

sorry, I don't understand what you mean about inefficiency and fundamental physics principles

if the centre of mass of the car is accelerating at some ##\ddot{\mathbf{x}} = (v^2 / \rho) \mathbf{e}_n##, then the net force on the car must be ##m\ddot{\mathbf{x}} = (mv^2 / \rho)\mathbf{e}_n##. the only external force on the car in such a situation, which can provide that force, is friction.

You now understand the difference between velocity and speed. Acceleration is a change in velocity. Acceleration, like velocity, is a vector so it has a direction as well as a magnitude. When acceleration is parallel to the velocity then it changes the speed. When acceleration is perpendicular to the velocity then it changes the direction of the velocity.

Force is proportional to acceleration. So in order to go in circular motion you need a force that is perpendicular to the velocity. That force is required in order to turn.

When a marble turns on a smooth track the force is perpendicular to the velocity. So a marble can turn without any additional push from behind. It only needs the push from the side given by the track.

When a car turns, because of how tires work, the force is not perfectly perpendicular to the velocity. There is a little bit of force going anti-parallel to the velocity. So you need a touch of gas to counteract that. You need the push from the side but also a bit of a push from behind due to the inefficiency of turning with tires.

PeroK, Delta2 and etotheipi
Dale said:
When a car turns, because of how tires work, the force is not perfectly perpendicular to the velocity. There is a little bit of force going anti-parallel to the velocity. So you need a touch of gas to counteract that. You need the push from the side but also a bit of a push from behind due to the inefficiency of turning with tires.

I think the key point to understand here is that no matter how complex the many different forces between the tyres and the road, the sum of all these forces from the road as well as of course the weight (which, neglecting the air, are the only net external forces on the car) is always proportional [parallel] to the acceleration of the centre of the mass of the car

jbriggs444, Delta2 and Dale
If you take a pinball and shoot it directly at (the inside of) a V, it will bounce off one arm, go sideways, bounce off the other, then run back where it came from, experiencing no loss of speed at any time. If you were inside the pinball, you'd get creamed at each bounce because of the massive instantaneous change in velocity.

Now shoot it at a U ; it slides down the inside, curves around the bottom, then procedes to roll back in the opposite direction. If you were inside that one you'd be much more comfortable, since the changing velocity (ie: acceleration) is spread out over time. Like the V example, the speed doesn't change throughout the procedure.

etotheipi said:
I think the key point to understand here is that no matter how complex the many different forces between the tyres and the road, the sum of all these forces from the road as well as of course the weight (which, neglecting the air, are the only net external forces on the car) is always proportional [parallel] to the acceleration of the centre of the mass of the car
Yes agreed.

I only explain about tires because if they actually do the experiment they will find that they do slow down. That isn’t because the theory is wrong, but because cars are complicated and messy machines. The marbles are simpler and easier to analyze. I always prefer simple experiments.

etotheipi
Dale said:
but because cars are complicated and messy machines. The marbles are simpler and easier to analyze. I always prefer simple experiments.

Yes, exactly! Much better to build up complexity gradually, rather than starting with an extremely complex mechanism like a car! There is much to be gained by carefully understanding the dynamics of a single particle, then generalising to a system of particles, then a system of interacting particles, continuous bodies etc.

e.g. your example of the marble is a much better tool to understand the general motion of a particle than the example with the car that the op kept referring to

Delta2 and Dale
DrStupid said:
That's what I'm talking about. The ISS is accelerated in classical physics but the accelerometer shows zero. It doesn't work this way.
"Shows zero" and "sums to zero" is the same thing here. I'll explain:
etotheipi said:
I don't really know what you mean by 'the two accelerations are aligned and subtract to zero' for the ISS case. When we're thinking in terms of GR and all that stuff, if we ignore the atmosphere then there's no force at all on the ISS (apart from the tidal forces, which we can ignore on the small scales), and so no proper acceleration. Rather than 'two accelerations cancelling', probably clearer to say that there was no proper acceleration in the first place.
• A stationary or constant speed car with a 3-axis accelerometer reads 1.0g upward acceleration.
• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.
• Now the car does the same "turn" in a loop. At the top of the loop, the accelerometer reads...

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russ_watters said:
• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.
A banked turn just means that there is less/none lateral tire friction needed, because the normal force has a centripetal component. If the trajectory of the car is still the same as for the flat track, the proper acceleration will be of the same magnitude.

Or do you mean the entire circular flat track is now on an inclined plane?

etotheipi
Acceleration can be resolved into tangential and normal component (check wikipedia link at bottom of this post). The tangential component has direction same as the direction of velocity, while the normal component has direction normal (or equivalently perpendicular) to the direction of velocity.

Seems like your Earth flat friend understands only tangential acceleration and completely ignores normal(or centripetal) acceleration. Tangential acceleration is what causes the velocity to change in magnitude (or simply for an object to speed up or down as you say) but normal acceleration is what causes the velocity to change in direction.

To sum it up: Velocity is a vector it has both magnitude and direction. Tangential acceleration changes its magnitude, normal acceleration changes its direction. Simple as that, tell that to your friend and let me know what he thinks about.

https://en.wikipedia.org/wiki/Acceleration#Tangential_and_centripetal_acceleration

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Silverbeam said:
But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?
Your basic mistake here is to try to understand the relative complexity of moving on a surface using an engine, rubber tires and friction on the surface - where accelerating, braking and turning are not trivial mechanical processes.

This is why physics is usually begun by studying Kinematics - studying motion without reference to the causes of motion. A good example is, of course, uniform circular motion. You learn about velocity and acceleration vectors, kinetic energy etc.

There is an interesting parallel here between your struggles and why it look until 1687 for someone (Isaac Newton) to formulate the laws of motion. No one previously had seen through the complexities of everyday motion to realize that there were basic fundamental laws governing all motion. And that there was a relationship between the motion of objects on Earth, and the motion of the planets around the Sun. For example, if we look at Newton's first law:

An object will remain at rest or move with constant speed in a straight line, unless acted upon by an unbalanced force.

This flew in the face of previous "Aristolelian" wisdom, which asserted that objects naturally slow down and need a force to keep them moving. And so, the hand of God was needed to keep the planets moving through the heavens, as it were.

Newton was the first to realize that any slowing down is the result of external forces. And, although we cannot avoid these forces on Earth, the movement of the planets do not slow because there are no dissipative forces like air resistance and friction. To quote Newton himself:

Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motion, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.

May I offer a personal view here that it is a tragedy that you, a 21st Century science student, are ignorant of this.

Note that I've underlined where Newton also pointed out that uniform circular motion (in the example of a top - which is an old-fashioned spinning toy) carries on indefinitely unless slowed by the air.

In short, you are making the same mistake as Aristotle and his disciples that energy is needed to maintain circular motion. But, Newton said otherwise in 1687. Note that:

a) A car, as explained above, is relatively inefficient at turning and will slow down relatively quickly.

b) A spinning top may continue for a few minutes perhaps, but air resistance gradually slows it down.

c) The Moon, having neither friction not air resistance to contend with, may continue its orbit about the Earth almost indefinitely.

This is very much the starting point for modern science.

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jbriggs444, Nugatory, DrStupid and 2 others
russ_watters said:
• A stationary or constant speed car with a 3-axis accelerometer reads 1.0g upward acceleration.
• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.
• Now the car does the same "turn" in a loop. At the top of the loop, the accelerometer reads...
I don't quite see what you're getting at here. To compute the proper acceleration in classical physics, you can just sum all of the forces except weight, and divide by the mass.

- The car stationary on the Earth's surface reads 1.0g upward acceleration since there's only an upward normal force on it
- When it does the hard turn, it has an upward normal force on it, and an inward frictional force on it, so the proper acceleration is, say, 1.4g at 45 degrees to the horizontal.
- If it does the turn on a frictionless banked track, it has a normal force with both an upward and horizontal component (this time the horizontal component is provided by the normal force, and not friction), and once again the proper acceleration is, say, 1.4g at 45 degrees to the horizontal
- At the top of the loop the loop, the normal force depends on how fast the car's going, and the proper acceleration will point downward toward the ground with some as of yet unknown magnitude.
- For the ISS, there's no forces at all, and its proper acceleration is zero.

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russ_watters said:
"Shows zero" and "sums to zero" is the same thing here.

Of course it is. The wording is irrelevant. The centripetal acceleration of the ISS cannot be measured with an accelerometer - no matter how you phrase it.

Dale
Well I didn't mean to start an argument, I was just bringing up the obvious fact that I can write the number 69 as 69 + 8 - 8 if I wanted to, and just add random stuff and subtract it again, but that's detracting from the point.

for the ISS it's not a case of 'two accelerations cancelling', it's a case of there being no proper accelerations at all in the first place. that seems pretty conceptually clear to me?

DrStupid
Silverbeam said:
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.

You're arguing semantics. Acceleration is not equal to the rate of change of speed. It's equal to the rate of change of velocity.

Ask your friend if he can drive his car in a circle on wet ice with bald tires. You need a force of friction between the tires and the road surface to move in a circle.

Acceleration is a change in the speed and/or the direction of an object. Both a change in speed or a change in direction require an external force. Ask your friend if there's any way to change the speed or direction of an automobile without applying an external force--either the force of friction from the front tires on a turn, or by gunning the engine to make the car go faster.

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