Inertia

paulb203 · 2025-04-14 23:05:17

Is inertia solely dependent on mass?

This is what I’m hearing, and I pretty much accept it, but I’m wondering why it isn’t also dependent on velocity.

Example.

We want to stop a 100kg trolley with a constant v of 6m/s in 2s;
F=ma
F=100kg(-3m/s/s)
F=-300N

Compared with the same trolley with a constant v of 12m/s (again, stopping it in 2s);
F=ma
F=100kg(-6m/s/s)
F=-600N

**

So it takes more F to stop the trolley when it’s moving faster. Why doesn’t this translate to; the trolley’s tendency to resist acceleration depends on, among other things, the trolley’s velocity?

Bob · 2025-04-15 08:25:51

Usually I can answer your questions based on what I was taught and passed on in my own teaching. This one is the exception. In all the Newtonian mechanics and physics questions I have encountered, inertia has never occurred.

I had to go up in my loft and get down all my old texts on applied maths and physics. Some just refer to Newton and basically say bodies possess the property of inertia, that is they do not accelerate unless acted upon by an external force.

I also tried googling the units for inertia. I got two answers:

Mass is a measure of an object's inertia. The more mass an object has, the more inertia it has.

The SI unit for inertia is kilogram-meter squared (kg⋅m²). While the term "inertia" is often used to refer to an object's resistance to changes in motion, the actual concept of resistance to change is often referred to as moment of inertia. The moment of inertia is a measure of how an object resists rotational acceleration.

The first is inertia as it applies to linear motion and the second to rotating objects.

The measure of linear kinetic energy is 1/5 . m . v^2 and for rotating objects 1/2 . I / w^2 where I is the moment of inertia and w the angular velocity.

We're not the only ones confused. Have a look at this thread :

https://physics.stackexchange.com/quest … n-stopping

So there we are. Everyone is confused and there's no one answer.

LATER EDIT: I've given this some over-night thought. For an object with zero or uniform velocity it's inertia is because of its mass. More mass, more inertia. It's actual velocity is irrelevant. The Earth rotates on its axis, and around the Sun, which in turn, rotates around the centre of the Galaxy, which is moving relative to other galaxies. That's why we have the concept of frames of reference.

If you consider that trolley going at various speeds, then, yes, the amount of force to reduce that velocity to zero will vary, but that doesn't alter its inertia. It just gives you the means to do the calculation. If you set up a frame of reference that travels at 6 m/s in the second case, then the trolley is only travelling at 6 m/s relative to that frame and so can be 'brought to rest' in the frame with the same effort as the first case.

Momentum gives you a way to measure the force required, but I showed in a previous post that impulse is just a way of applying v = u + at to determine F.

Bob

paulb203 · 2025-04-18 22:24:35

Thanks, Bob, for going above (literally; to the loft) and beyond.

Yes, there does seem to be a lack of consensus regards the concept of inertia.

I've heard more than one person say that it's not a well-defined technical term in physics. And others saying it tend to come up early on for students and

then they hear of it less and less.

As for a unit (for inertia regards linear motion) most seem to be saying there isn't a unit, with a few saying that it's kg, as inertia is equivalent to mass.

paulb203 · 2025-04-18 22:26:38

Bob, you said,

“The Earth rotates on its axis, and around the Sun, which in turn, rotates around the centre of the Galaxy, which is moving relative to other galaxies. That's why we have the concept of frames of reference.”

Wouldn’t we have reference frames without all of that? Wouldn’t we have reference frames if the Universe consisted solely of a static Earth?
On a static Earth you could still, for example, be seated on a railway platform, at rest with reference to the person sharing the bench with you; while a person on a moving train, at rest with reference to the person sharing the seat with her, would be moving with reference to you; and they could see themselves as at rest with you moving away from them. And someone could be running along the aisle of the train to catch the buffet car before it closed, etc, etc. Wouldn’t that amount to several reference frames?

Bob · 2025-04-18 23:50:14

Oh yes,certainly. I just used those as examples. There's no limit to the number of possible frames.

Bob

paulb203 · 2025-04-20 23:16:52

“I just used those as examples. There's no limit to the number of possible frames.”

Thanks, Bob. I thought that might be the case, but wanted to be sure.

“If you set up a frame of reference that travels at 6 m/s in the second case, then the trolley is only travelling at 6 m/s relative to that frame”

Do you mean something like;

Train heading west at 6m/s relative to ground.
Trolley on platform heading west at 12/ms relative to ground.
Trolley in reference frame of train = 6m/s west
(12m/s – 6m/s)?

Bob · 2025-04-20 23:37:08

That's exactly what I meant.

Bob

paulb203 · 2025-04-21 23:08:42

Thanks, Bob

So now we view the trolley in the second example in the reference frame of the train moving at 6m/s in the same direction as the trolley.
To stop the trolley in 2s;

F=ma
F=100kg(-3m/s/s)
F=-300N

But if we view the trolley in the second example in the reference frame of the train why not view the trolly in the first example from that reference frame?
It was moving at 6m/s with reference to the ground. Now it’s moving at 0m/s with reference to the train.
But we still want to stop it in 2s.
So,

F=ma
F=100kg(a)

What do we put for ‘a’?

A=(v-u)/t
A=(0-0)/2
A=0/2
A=0

So,

F=100kg(0)
F=0N
But we know that a force of >0N would be required to stop the trolley, don’t we?

Bob · 2025-04-22 01:32:46

No. In that frame it is stopped so no force is needed.

Bob

paulb203 · 2025-04-23 22:02:52

Fascinating. And mind-bending. For me at least.

So you, Bob, are driving a train, east at 6m/s.

And I’m driving a trolley east at 6m/s, parallel to you.

From the reference frame of your train I’m at rest.

And in your reference frame no force is required to stop me, because I’m already at rest? Even though we both know a force would be required to stop me in the reference frame of the ground beneath me?

Bob · 2025-04-24 05:24:33

It has to be like that because of all the other motions that we're all involved in. eg. the Earth is hurtling through space (could estimate the speed but hopefully my point stands without that). If you had to stop that speed too you'd need a lot of force just to take the dog for a walk!

Bob

paulb203 · 2025-04-25 23:26:09

Thanks, Bob.

Returning to,

"“If you set up a frame of reference that travels at 6 m/s in the second case, then the trolley is only travelling at 6 m/s relative to that frame and so can be 'brought to rest' in the frame with the same effort as the first case.”

What if we then look at a trolley travelling at 9m/s in the ground reference frame, and therefore travelling at 3m/s in the train reference frame?

Now, to stop the respective trolleys in 2s, we have;

Trolley A (6m/s in the train reference frame)

F=ma
F=100kg(-3m/s/s)
F=-300N

Trolley B (3m/s in the train reference frame)

F=ma
F=100kg(-1.5m/s/s)
F=-150N

So, in the train reference frame, we have two trolleys OF THE SAME MASS, (100kg), but more force is required to stop one than is required to stop the other, due to their different velocities.

Bob · 2025-04-26 00:16:42

Yes, that looks good.

B

paulb203 · 2025-04-27 23:04:51

Thanks, Bob.

I asked chatgpt about it.

I said,

"If inertia is 'an object's tendency to resist acceleration', and increasing velocity alters that tendency, then inertia must depend, at least partially, on velocity."

It replied with,

"And you're not wrong — if we use that broad, intuitive definition of inertia.

And then it got complicated, with how Newton actually defined things like mass, and acceleration, in terms of F=ma, etc.

I think I'll leave it for now, let it brew, and come back to it later. Thanks for your help with this one.

Bob · 2025-04-27 23:58:16

chatgpt wrote:

increasing velocity alters that tendency,

Wrong! It doesn't. The bot is confusing actual velocity with how much we want to alter the velocity. It takes more effort if we want to alter velocity a lot, but Newton's law just says velocity stays constant until we apply an external force. The amount of force determines how much the velocity changes but the start velocity is irrelevant. That's why we have frames of reference; otherwise we've got to take account of all the possible velocities (orbits, movement of galaxies etc.)

It takes the same force to change velocity from say 10 m/s to 5 m/s whether the start velocity is 10 m/s or 10 million m/s.

Conclusion: Don't trust bots to tell you anything.

Bob

KerimF · 2025-04-28 17:44:58

Bots are said having AI because they are programmed to learn from humans, besides being an archive (sort of encyclopedia) of what are known by humans universally.

Bob · 2025-04-28 19:36:59

I tried again to research this. Mathsword doesn't list inertia. Wolfram Alpha didn't recognise my question.

I googled "Is inertia the same as mass "

The google AI bot had this to say:

No, inertia is not the same as mass, but mass is a measure of inertia.
Mass is a fundamental property of matter that quantifies the amount of material in an object.
It is measured in kilograms (kg).
Inertia is the resistance of an object to changes in its state of motion. An object with more mass has more inertia, meaning it takes more force to change its velocity (speed or direction).
Mass is the measure of an object's inertia. A larger mass means a greater resistance to changes in motion, which is the essence of inertia.
Generative AI is experimental.

I then tried "does inertia depend on velocity"

google AI wrote:

Inertia, which is an object's resistance to changes in its state of motion, does not depend on velocity. Inertia is a property of an object determined solely by its mass. While velocity does play a role in how an object resists changes in motion through momentum, inertia itself is independent of how fast an object is moving.

Bob

Math Is Fun Forum

#1 2025-04-14 23:05:17

Inertia

#2 2025-04-15 08:25:51

Re: Inertia

#3 2025-04-18 22:24:35

Re: Inertia

#4 2025-04-18 22:26:38

Re: Inertia

#5 2025-04-18 23:50:14

Re: Inertia

#6 2025-04-20 23:16:52

Re: Inertia

#7 2025-04-20 23:37:08

Re: Inertia

#8 2025-04-21 23:08:42

Re: Inertia

#9 2025-04-22 01:32:46

Re: Inertia

#10 2025-04-23 22:02:52

Re: Inertia

#11 2025-04-24 05:24:33

Re: Inertia

#12 2025-04-25 23:26:09

Re: Inertia

#13 2025-04-26 00:16:42

Re: Inertia

#14 2025-04-27 23:04:51

Re: Inertia

#15 2025-04-27 23:58:16

Re: Inertia

#16 2025-04-28 17:44:58

Re: Inertia

#17 2025-04-28 19:36:59

Re: Inertia

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