UKC

As I (Wikipedia) understand it Newton's first law states that, "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force."

I'm struggling with this in reference to a situation which came up in an A Level physics lesson. Imagine a still light, rod with a force acting at either end of it, the forces are equal and one is acting "up" and the other "down". This rod would spin around the centre point.

Now imagine that both the up force and the down force are acting at the centre of the rod. This rod would remain still.

In both situations there is an external force, in both situations the up = the down, so according to my understanding of N1L, the outcome should be the same.

What am I missing? I presume that there is something in the definition of "an external force" which means situation 1 has an external force and situation 2 doesn't. Or is it something to do with the "inertial reference frame" which I don't fully understand?

Thanks for any input, it's fried my brains a bit.

In reply to ablackett:

In your scenario, it doesn't have an external force acting on the rod but two external forces.

In reply to ablackett:
The law should state "resultant" external force. As the two forces are equal they cancel each other out so there is no change in velocity.

Unless of course one is greater, in which case the rod would move sideways in the direction of that force.

In reply to ablackett:

As above, in both cases the resultant linear force is zero and the outcome *is* the same in that the centre-of-mass of the rod doesn't move.

But in the second case the resultant *torque* is not zero, so the rod spins.

In reply to ablackett:

Every couple has its moments

In reply to ablackett:

Fried my brain as well. As long as it catches fish, what does it matter? Ring spacing and taper will vary between spinning rods.

In reply to ablackett:

The other replies about the centre of mass staying stationary answer one part of the issue, but for the reason why it rotates, you can view it as follows. The upwards force on one end of the rod causes the atoms at that end to start moving upwards. The downwards force on the other end forces the atoms at that end to start moving downwards. The forces between the atoms in the rod cause the atoms at both ends to continue to be pulled towards the middle of the rod, and the atoms they're next to to be pulled up or down. In the end the resultant force on all the atoms results in the rod as a whole moving in a circle.

In reply to rka:


Wrong thread - back to marriage again

In reply to ablackett:

Get yourself on the ISS, then you can try it out.

In reply to ablackett:

Wasn't it Issac Walton not Newton that was the fisherman?

In reply to elliptic:


So is the definition of a "external force" that either, the resultant linear forces are non zero or the resultant torque is non zero. If so I didn't realise the second bit was part of the definition and that's my problem.

In reply to ablackett:
From the original Latin of Newton's Principia:

“ Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. ”

Translated to English, this reads:

“ Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.[28] "

I'm happier with that translation, my spinning rod has a force which compels it to change state. That removes any tricky definition of what a resultant force is, as a resultant force (or external force, or unbalanced force) is essentially a force which compels something to change state.

In reply to ablackett:


Do you have the Latin to add: 'always assuming the body is not freely suspended at the end of a 50m climbing rope'?

In reply to ablackett:

I don't think that makes it clearer.

What's confusing you is that in their basic form, Newton's laws are about objects that can be treated as point masses with forces acting through CoMs. You're not dealing with that, you have an extended object and offset forces.

As I said before, in both cases the resultant linear force is zero, the difference is that the rod that spins has had a *torque* applied because the two external forces are not acting through CoM.

In reply to elliptic:

Ah, so it's my understanding of Newtons "object" which is wrong, not his force.

In reply to Dave Garnett:


'ratione tamen habita corpus non libere appenditur in finem a 50m funem scandens'

In reply to ablackett:


Assuming a spherical chicken in a vacuum ...

In reply to zebidee:


'pro fune scandens' perhaps, but then I'm only cheating with Google translate!

In reply to ablackett:


Very unclear statement. If the rod is say, vertical, with the top force acting downwards and the bottom force acting upwards then the point of equilibrium is extremely small and any slight imbalance will result in a vector inducing rapidly increasing turn. Is that what you mean?

Or do you mean the rod is horizontal with an up force at one end and a down force at the other?

In reply to digby:



Yes, that one.

In reply to ablackett:

So I either don't understand Inertial referance frames, or I don't understand objects, I don't understand acceleration, or I don't understand resultant forces.

Or perhaps a bit of all 4!

In reply to ablackett:

Then you can't ignore the fact that the rod is rigid, pivoted about a centre point, and subject to two external forces not in direct opposition. Thus not cancelling each other out. They have the effect of accelerating the ends of the rods in opposite directions, and since the rod is rigid, spinning it.

In reply to digby:

That's obvious intuitively. The OPs question though is answered by the law applying to point masses rather than extended objects

In reply to ablackett:

I think Newton's 3 laws are best thought of as applying to point masses (the first law being a special case of the third law). It is then possible to prove from them that, for any collection of point masses (which could be a rigid body, a flexible body or any thing else!), that Newton's first and third laws apply to the Centre of Mass and external forces, and that, in addition, the rate of change of angular momentum about the Centre of Mass is equal to the total moment of the external forces about the Centre of Mass.

In reply to Robert Durran:

See! I knew someone with the right answer would come along!

In reply to ablackett:

Force is a vector. So it has direction as well as an amount. Your forces at each end don't cancel each other out because of this.

In reply to marsbar:
Yes they do. Same magnitude, opposite direction. The vector sum is zero - forces are free vectors.

In reply to MG:
Then why does it spin?

(My physics is very rusty)

In reply to marsbar:

See ecliptic's posts above. There is torque applied to the extended body. If viewed as a collection of connected point masses, N1L applies to each mass (I think - not a physicist...)

In reply to MG:

You're right, Newtons laws do apply to each of the point masses making up the rigid rod.