# Rings on a rod: angular momentum conceptual question

• omega5
In summary, a uniform rod with two small rings attached is rotating in a horizontal plane at an angular velocity of 33.0rev/min. When the rings are released and slide outward along the rod, they carry away mass and angular momentum. However, the remaining rod maintains the same angular velocity due to conservation of angular momentum. This is because the mass and angular momentum carried away by the rings are equal to the mass and angular momentum they contributed to the system before departure. Therefore, the mass and angular momentum of the rod remain unchanged, resulting in no change in its angular velocity.
omega5

## Homework Statement

A uniform rod of mass 3.15×10−2kg and length 0.380m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.250kg , are mounted so that they can slide along the rod. They are initially held by catches at positions a distance 5.20×10^−2m on each side from the center of the rod, and the system is rotating at an angular velocity 33.0rev/min. Without otherwise changing the system, the catches are released, and the rings slide outward along the rod and fly off at the ends.

a) What is the angular speed of the system at the instant when the rings reach the ends of the rod?
b) What is the angular speed of the rod after the rings leave it?

## Homework Equations

$I_1 \omega_1 = I_2 \omega_2$

## The Attempt at a Solution

I got the problem right but want to understand what's going on. I used conservation of angular momentum to calculate the angular velocity when the rings reached the end, but apparently the system has the same angular velocity after the rings leave. How does that work? Doesn't the mass and moment of inertia go down since it's only the rod in the case b?

omega5 said:
the system has the same angular velocity after the rings leave. How does that work? Doesn't the mass and moment of inertia go down since it's only the rod in the case b?
When the rings depart, they carry away mass and angular momentum. These are the same mass and angular momentum they contributed to the system total the instant before departure. Therefore the mass and angular momentum that remain are those the rod had the instant before departure. Why would the angular speed of the rod change?

omega5
Thank you! I understand now. Sounds dumb, but I neglected that angular velocity. Under my assumptions, the rings would have just fell straight down after they reached the ends of the rod. That defies inertia.

## What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity that measures the amount of rotational motion an object has around a fixed axis.

## What causes an object to have angular momentum?

An object has angular momentum when it is rotating around a fixed axis. This can be caused by an external force, such as a torque, acting on the object.

## How is angular momentum different from linear momentum?

Angular momentum and linear momentum are both measures of motion, but they differ in the type of motion they describe. Linear momentum is a measure of an object's motion in a straight line, while angular momentum is a measure of an object's rotational motion.

## How can the angular momentum of an object change?

The angular momentum of an object can change when an external torque is applied to it. This can cause the object to speed up or slow down its rotation, thus changing its angular momentum.

## What is the conservation of angular momentum?

The conservation of angular momentum states that in a closed system, the total angular momentum remains constant. This means that the amount of angular momentum in a system will not change unless an external torque is applied.

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