# Angular momentum conservation and constant velocity as expla

• Soren4
The correct way to think about the deviation is not by considering the tangential velocity, but by realizing that the ball continues to have the same linear velocity while moving in a curved path, resulting in a deviation from the expected straight line. In summary, the angular momentum of the ball is conserved with respect to the center of the carousel, while the tangential velocity is not. The deviation in the rotating frame can be explained by the fact that the ball maintains the same linear velocity while moving in a curved path. Both descriptions, the one based on greater tangential velocity and the one based on conservation of angular momentum, are equivalent but the latter is more accurate.

#### Soren4

I'm confused about situations involving rotating frames in which the angular momentum is conserved and the initial velocity does not change. I'll make an example.

Take a rotating carousel (constant angular velocity) with no friction on it and a ball. At the initial time instant the ball has the same velocity of the carousel and is far from the center ##O##. It is given a radial impulse, so that it gains a radial velocity also.

In a inertial frame the path of the ball is a straight line, while in the rotating frame it is deviated by Coriolis force.

The angular momentum of the ball is conserved with respect to ##O## in the inertial frame. Nevertheless I read many times that the "deviation" in rotating frame can be explained if we think about the fact that the ball has a greater tangential velocity than the rest of the carousel, so it appears to go faster.

So on the one side we have that, taking the center of the turntable ##O## as pivot ##L=mrv_{\theta}=mr^2\omega## is conserved, on the other hand that the initial velocity ##v= \omega r## does not change.

Neglecting ##m##, saying that ##r^2 \omega## and ##r \omega## are constant is definitely not the same thing. But are both of them conserved in this case?

In this kind of situation are the two description (the one that uses the fact of greater velocity and the other that is based on the conservation of angular momentum) equivalent?
Is there one more correct to use?

Soren4 said:
So on the one side we have that, taking the center of the turntable ##O## as pivot ##L=mrv_{\theta}=mr^2\omega## is conserved, on the other hand that the initial velocity ##v= \omega r## does not change.

Neglecting ##m##, saying that ##r^2 \omega## and ##r \omega## are constant is definitely not the same thing. But are both of them conserved in this case?
##r\omega## is not conserved, because that is the tangential component of velocity, which does not remain constant. As the ball, after release, moves further away from the carousal centre, its linear velocity ##v## remains constant, but the radial component increases and the tangential component decreases, as they are functions of position.

##r^2\omega## is conserved however. Angular momentum is still meaningful, and is still conserved, when a body is not in circular motion.

• Soren4

## 1. What is angular momentum conservation?

Angular momentum conservation refers to the principle that the total angular momentum of a closed system remains constant, provided there are no external torques acting on the system. This means that the rotational motion of a system will not change unless an external torque is applied.

## 2. How is angular momentum conserved?

Angular momentum is conserved through the law of conservation of angular momentum, which states that the total angular momentum of a system must remain constant in the absence of external torques. This means that any changes in the rotational motion of a system must be offset by equal and opposite changes in the rotational motion of other objects in the system.

## 3. What is the relationship between angular momentum and velocity?

Angular momentum and velocity are related through the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. This means that an increase in angular velocity will result in an increase in angular momentum, and vice versa.

## 4. How does constant velocity relate to angular momentum conservation?

In the absence of external torques, constant velocity is directly related to angular momentum conservation. This means that if an object is moving at a constant velocity and there are no external torques acting on it, its angular momentum will remain constant.

## 5. Can angular momentum be created or destroyed?

No, according to the law of conservation of angular momentum, angular momentum cannot be created or destroyed. It can only be transferred from one object to another within a closed system. This is similar to the conservation of energy, where energy can be transferred but cannot be created or destroyed.