# Conservation of Momentum not universal?

• CHUKKY
In summary, angular momentum is not conserved in every reference frame, but it is conserved when there is a net torque on the system.

#### CHUKKY

So I calculate the momentum of a body moving with a constant speed along a circular path with mass m, tangential velocity v and radius r. Its angular momentum is mvr.kk. Good. Now what if I calculate the angular momentum from a point on the path of the circle. A simple calculation shows that the angular momentum about a point vertically below the center of the circle and which is also on the path of the circle is different for the particle at two different points. e.g. at the the point where the radius of the circle makes an angle with the positive x-axis and the point where the radius of the circle makes an angle zero with the x axis. at the 90 degree point it is 2mvr and at the 0 degree point it is mvr. So does this mean that angular momentum is not conserved in every reference frame?

For circular motion there must be a constant force of $\frac{mv^2}{r}$ towards the center of the circle. When you take your reference frame as the center of the circle then there is no net torque since the force vector is parallel to the position vector, however when you move your reference frame to any other point there will be net torques over parts of the motion.
The key then is to try to pick a reference frame with the least torques involved.

"The key then is to try to pick a reference frame with the least torques involved." so what ur saying is that indeed I did not make a mistake and the momentum is not conserved in all inertial reference reference frame. But I thought the laws of physics were meant to be the same in all inertial refrence frame. So what this means is that in one frame of reference angular momentum is conserved and in another frame of reference angular momentum is not conserved. Or perhaps I am missing the theory. Ok can we say that the laws of physics are universal in that the actual law in analysis should have been that in the absence of a torque, angular momentum is conserved. So since torque was present angular momentum would not be conserved. So is that what it means? You know this is one clear way in which angular momentum differs from linear momentum. In linear momentum, momentum is always conserved in all reference frame.

Angular momentum is only conserved for systems with no net torque on them. That's why if you choose the center point, the angular momentum is conserved, because the force goes through that point and the torque is zero. But if you choose a point on the circle, the force doesn't go through that point, so the torque is not zero. Nonzero torque causes a change in angular momentum. The conservation is only reestablished when you look at the larger system that includes whatever is supplying that torque. A closed system (one with no external forces on it) must have no net torques on it either, so a closed system will always conserve angular momentum. Open systems only do if they are open in such a way that does not experience any net torque, and that's the only issue that is frame-dependent-- the external torque is frame dependent on an open system like something going in a circle.

This is a valid observation and it does appear that angular momentum is not conserved in every reference frame. However, this does not mean that the principle of conservation of momentum is not universal. Conservation of momentum is still a fundamental law of physics that holds true in most cases. In this scenario, the difference in angular momentum can be attributed to the different reference points used for calculation.

In order for the principle of conservation of momentum to hold true, the system must be isolated and there must be no external forces acting on it. In this case, the particle is moving along a circular path and there is a centripetal force acting on it, which is provided by the tension in the string. This force is directed towards the center of the circle and its magnitude is given by mv^2/r. Since this force is not acting on the particle at the two different points, the system is not truly isolated and the principle of conservation of momentum does not apply.

Additionally, it is important to note that angular momentum is a vector quantity and its direction also plays a role in its conservation. In this scenario, the direction of the angular momentum changes as the particle moves along the circular path, further contributing to the difference in its value at different points.

In conclusion, while it may seem that angular momentum is not conserved in every reference frame, it is important to consider all the factors at play in a given system. In most cases, conservation of momentum holds true and it is a fundamental principle in understanding the behavior of physical systems.

## 1. What is the conservation of momentum?

The conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

## 2. Why is conservation of momentum not universal?

The conservation of momentum is not universal because it only applies to isolated systems where there are no external forces acting on the system. In real-world situations, there are often external forces present that can change the momentum of a system, making it not completely conserved.

## 3. What are some examples of conservation of momentum not being universal?

One example is when a rocket is launched into space. The rocket's momentum changes due to the force of the rocket engines, which are external to the system. Another example is when a car crashes into a wall. The car's momentum changes due to the external force of the wall.

## 4. How does the law of conservation of energy relate to the conservation of momentum?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This is related to the conservation of momentum because when momentum is not conserved, it means that energy is being transferred or converted, violating the law of conservation of energy.

## 5. Can conservation of momentum ever be violated?

In isolated systems where there are no external forces present, the conservation of momentum will always hold true. However, in real-world situations, there can be external forces that can change the momentum of a system, making it not completely conserved. This can make it seem like the conservation of momentum is being violated, but in reality, it is just not applicable to the specific situation.

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