# Conservation of linear momentum in this system

• undividable
In summary: The axleIn summary, the mouse moves north on a stationary turntable, which is supported by a frictionless vertical axle. The axle has finite mass and will move south along with the wheel while the mouse moves north.
undividable
A pet mouse sleeps near the eastern edge of a stationary, horizontal turntable that is supported by a frictionless,
vertical axle through its center. The mouse wakes up and starts to walk north on the turntable. Is the momentum of the system constant?
i understand that the initial momentum is zero, because the turntable and the mouse have v=0, and that the final momentum is not zero, since v≠0 for the mouse, and v=0 for the turntable, so linear momentum is not conserved, but since ∫∑Fext dt=dp, where is the external netforce (∑Fext) that causes the change in the system's momentum? It seems to me there are none. only internal forces (friction) between the mouse and the turntable

undividable said:
where is the external netforce (∑Fext) that causes the change in the system's momentum
The axle

Dale said:
The axle

so, as the mouse moves upward, the axle exerts and external force (normal downward force) on the turntable so it stays with v=0? and if the axle was a part of the system? the linear momentum should still change, but now the external net force would be is 0

undividable said:
so, as the mouse moves upward, the axle exerts and external force (normal downward force) on the turntable so it stays with v=0? and if the axle was a part of the system? the linear momentum should still change, but now the external net force would be is 0
If the axle has finite mass, it will move south along with the wheel while the mouse moves north. Net linear momentum of the system (including axle) remains zero.

If the axle has infinite mass, it is an infinite momentum sink. Its momentum cannot be calculated by measuring zero velocity and crying "Eureka: zero momentum".

undividable said:
and if the axle was a part of the system?
Then identify the forces acting on the axle and apply Newton's laws.

## 1. What is conservation of linear momentum?

Conservation of linear momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant, unless acted upon by an external force. This means that the total mass and velocity of the system before and after a collision or interaction will be the same.

## 2. How is linear momentum calculated?

Linear momentum is calculated by multiplying an object's mass by its velocity. The formula for linear momentum is p = mv, where p is momentum, m is mass, and v is velocity.

## 3. What is an example of conservation of linear momentum in action?

A common example of conservation of linear momentum is a billiards game. When the cue ball hits another ball, the total momentum of the system remains constant. The cue ball loses momentum, while the other ball gains momentum, resulting in a change in velocity for both balls.

## 4. What are some real-world applications of conservation of linear momentum?

Conservation of linear momentum has many applications in the real world, including in collisions between vehicles, projectiles, and even in sports such as football and hockey. It is also essential in the design and operation of vehicles and spacecraft.

## 5. Are there any exceptions to conservation of linear momentum?

While conservation of linear momentum is a fundamental principle, there are some exceptions to this rule. In extremely small scales, such as at the atomic and subatomic level, quantum mechanics plays a significant role, and momentum may not be conserved. Additionally, in systems that involve external forces, such as rocket propulsion, linear momentum may not be conserved.

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