# Conservation of momentum and isolated systems

• WY
In summary, angular momentum and rotational kinetic energy are seldom conserved simultaneously in isolated rotational motion.
WY
I was reading on the conservation of momentum and they mention how in isolated systems momentum is always conserved and if the external forces of the system is zero. In the case of friction or drag acting against the motion of a body would that be considered as part of the isolated system or an external force not equalling to zero? Would momentum for the body be conserved? for example a boat at constant velocity is subjected to a drag force due to water resistance

when a star like a neutron star begins to collapse as it gets smaller and more gravity is pushed together it begins to spin faster a lot like how a ice skater spins faster as she brings her arms in, this is conservation of energy in a system with no external forces acting upon it, the conservation of momentum(angular) is constant.look at Newtons second law of planetary motion

The cahnge of motion of a body is proportional to the force acting on it and is made in the direction in which that force is acting(this is Newtons second law)

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WY said:
I was reading on the conservation of momentum and they mention how in isolated systems momentum is always conserved and if the external forces of the system is zero. In the case of friction or drag acting against the motion of a body would that be considered as part of the isolated system or an external force not equalling to zero? Would momentum for the body be conserved? for example a boat at constant velocity is subjected to a drag force due to water resistance

Friction or drag is not part of the "system" that is considered, so yes, that would be considered as an external force. Your "boat" is the body, and the water acts as an external medium for an external force on the boat. So your boat is no longer an isolated system.

Mariko: I've read two of your responses so far (the other one being on EM wave), and I would strongly suggest you double check them because they full of errors. For example, angular momentum and rotational KE are seldom conserved simultaneously in isolated rotational motion (one has Iw dependence, the other Iw^2 dependence - so think about it).

Zz.

WY said:
I was reading on the conservation of momentum and they mention how in isolated systems momentum is always conserved and if the external forces of the system is zero.
That's right. By "isolated system" we mean a system that does not interact with the rest of the world. At best, an isolated system can only be approximated. And, isolated or not, if the net force on a system is zero, then its total momentum will not change.

In the case of friction or drag acting against the motion of a body would that be considered as part of the isolated system or an external force not equalling to zero? Would momentum for the body be conserved?
Whether friction is an internal or external force on a system depends on how you define your system. If whatever is creating the friction is not part of your system, then momentum of the system is not conserved. For example: slide a block across a rough floor. If I take the block as my system, then it is not isolated (the floor exerts an external force on the block) and its momentum is not conserved. But, if I include the floor (and the rest of the Earth attached to it) as all being part of one giant system, then the momentum of that system is conserved (at least with respect to the friction between floor and block).
for example a boat at constant velocity is subjected to a drag force due to water resistance
If the boat is your system, then it is not isolated, since the water exerts a force on it. Of course, if the velocity is constant (in which case another force must be acting to cancel the drag; for example: the motor is running or wind is in the sails) then by definition the momentum is constant.

What is usually of interest is what happens when things interact. Let's say two objects collide. If you can ignore outside influences for the brief duration of the collision, then one can say that the total momentum of the system composed of both objects is conserved during the collision. (Since the only forces are those they exert on each other.) This is a very useful physical principle with many applications.

Thanks you!

Thanks to everyone for your help in making this so much clearer to me!

## 1. What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant, unless acted upon by an external force.

## 2. What is an isolated system?

An isolated system is a physical system that does not interact with its surroundings, meaning that no external forces or energies are acting on it.

## 3. How is momentum conserved in an isolated system?

In an isolated system, the total momentum remains constant because any changes in momentum within the system are balanced by equal and opposite changes in momentum of other objects within the system.

## 4. What are some real-life examples of conservation of momentum?

Some examples of conservation of momentum in everyday life include a billiard ball breaking a rack of balls, a person jumping off a boat and the boat moving in the opposite direction, and a rocket launching off the ground.

## 5. What are the implications of conservation of momentum for engineering and technology?

Conservation of momentum is an important principle in engineering and technology, as it must be taken into account when designing systems and machines. It helps engineers understand how forces and motion are related and allows them to predict and control the movement of objects in various systems.

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