# When are the initial and final momentums the same (conserved)?

• I
• annamal
In summary: If you draw the system boundary somewhere in the fuel and oxidizer lines...yes, the rocket would then have a net external force.

#### annamal

In a system with no external force like gravity, the final and initial momentums are conserved.
If we have a firework that explodes radially (disregarding gravity), the momentum before the explosion should equal the momentum after explosion. But isn't the explosion caused by an external force?

annamal said:
But isn't the explosion caused by an external force?
No - the gunpowder is in the rocket. Nothing outside the system is involved.

vanhees71
So whatever force is inside of an object is not an external force but an internal force?

That seems a bit circular. The question is: is there any interaction with anything outside the system? If not, momentum is conserved.

For example, if I bounce a ball off the wall the momentum of the ball goes from +mv to -mv. Momentum is not conserved, because the ball interacted with a wall and I didn't bother to track the momentum carried away by the (slight!) recoil of the wall. We call that an external force because we just concern ourselves with the effect on our system (the ball)and ignore the effects on things external to our system (the wall). In your rocket explosion case, though, there's nothing interacting with the rocket. All forces act on one part of the system and have an equal and opposite reaction on another part of the system (i.e., it's all internal) so the net momentum change is zero.

vanhees71
annamal said:
So whatever force is inside of an object is not an external force but an internal force?
It's an important aspect of Newton's third law that if something at rest explodes into two parts, then the parts have equal and opposite momentum.

Likewise, if it explodes into many parts, then the total momentum of all the parts added together is zero.

vanhees71
Ibix said:
That seems a bit circular. The question is: is there any interaction with anything outside the system? If not, momentum is conserved.

For example, if I bounce a ball off the wall the momentum of the ball goes from +mv to -mv. Momentum is not conserved, because the ball interacted with a wall and I didn't bother to track the momentum carried away by the (slight!) recoil of the wall. We call that an external force because we just concern ourselves with the effect on our system (the ball)and ignore the effects on things external to our system (the wall). In your rocket explosion case, though, there's nothing interacting with the rocket. All forces act on one part of the system and have an equal and opposite reaction on another part of the system (i.e., it's all internal) so the net momentum change is zero.
but if we analyze my rocket explosion case with the environment as a system, the rocket would then have a net external force?

annamal said:
but if we analyze my rocket explosion case with the environment as a system, the rocket would then have a net external force?
I don't understand what situation you propose to analyse. What do you think the external force is?

annamal said:
In a system with no external force like gravity
Gravity can also be an external force. That depends on system you choose to consider.
Forces of interaction between the parts of the system are the internal forces. Forces that act on the system from the objects outside the system are the external forces.

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vanhees71 and PeroK
Ibix said:
I don't understand what situation you propose to analyse. What do you think the external force is?
To reword it, which objects are in a system so that a rocket propelling forward becomes a net external force.

annamal said:
To reword it, which objects are in a system so that a rocket propelling forward becomes a net external force.
What scenario are we talking about? Most vehicles use an external force: walking, cycling, driving a car push against the ground and use the external reaction force to propel themselves (Newton's third law again). Boats use the water (or the wind). Aircraft use the air to generate an external force. A rocket is the exception, in that it tends to propel itself by firing expellant out the back. If you include the expellant as part of the rocket, then that is a internal force. If, however, you consider the expellant no longer part of the rocket, then the process looks like an external force on the remaining mass of the rocket.

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Ibix
annamal said:
To reword it, which objects are in a system so that a rocket propelling forward becomes a net external force.
No matter what system you consider, a rocket cannot become a force. At least not for the definition of "force" as used in mechanics.

If the propelling force on the object comes from outside the object we don't call it rocket.

Vanadium 50 and PeroK
nasu said:
No matter what system you consider, a rocket cannot become a force. At least not for the definition of "force" as used in mechanics.
If you draw the system boundary somewhere in the fuel and oxidizer lines leading to the combustion chamber then the hot and high pressure gasses are outside the system. Their pressure on the combustion chamber and the expansion bell then amounts to an external force.

If you draw the system boundary in the exhaust stream just aft of the expansion bell then there is little force acting across the system boundary. However, there is a high speed mass flow. A high speed mass flow across a system boundary means a momentum flow across that boundary. The notion of "force" can be interpreted broadly as a momentum flow.

No matter what physical quantity you associate with force, the rocket is not "it". Is not a force neither momentum flow. Same as the rocket is not a length even if you can measure its length and is not time even it takes time for the rocket to travel between different point.
It may be a force acting on the rocket but the rocket is not the force.

nasu said:
No matter what physical quantity you associate with force, the rocket is not "it". Is not a force neither momentum flow. Same as the rocket is not a length even if you can measure its length and is not time even it takes time for the rocket to travel between different point.
It may be a force acting on the rocket but the rocket is not the force.
What is the force then? The fire emitting out of the rocket?

annamal said:
What is the force then? The fire emitting out of the rocket?
The force is the push of the exhaust gasses on the craft and of the craft on the exhaust gasses.

nasu and Ibix
"Force" is a physical quantity that measures interactions between systems. It is not an object. It is not the rocket or any part of the rocket or the environment. The interaction between the exhaust gas and the rest of the rocket is measured by the quantity we call force. Neither of them is the force.

Ibix and PeroK