# Conservation of Angular Momentum - Problem understanding this scenario

• B
• jonhswon
jonhswon
Hello,

As far I know, in a closed system both, linear and angular monentums, are conserved.

İmagine such a scenario: everything is motionless, both momentums zero initially, then from a disk are fired (compressed spring push) two equal mass balls at same speed but opposite direction. Now balls fly away and disk is spinning. Linear momentum after firing is still zero, but angular momentum is not? What is happening?

(All usual assumptions in place, inertial reference, massless springs, etc..)

Last edited:
jonhswon said:
angular momentum is not
Have you taken into account the angular momentum of the balls?

vanhees71 and PeroK
... an object moving in a straight line at constant velocity has angular momentum about any point not on the line of motion.

Note also that angular momentum is always measured relative to some point.

vanhees71 and Ibix
OMG I was so blind. Thanks a lot !

I first had this discussion the other way round when a classmate at university lobbed a shoe at the door to shut it. It's quite neat how the changing tangential component of linear velocity cancels with the changing radial distance to produce a constant angular momentum for an object in linear motion.

vanhees71

## What is the principle of conservation of angular momentum?

The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. This means that the initial angular momentum of a system will be equal to its final angular momentum, provided no external forces are acting to change it.

## How does conservation of angular momentum apply to rotational motion?

In rotational motion, conservation of angular momentum means that the product of the moment of inertia and the angular velocity of a rotating object remains constant if no external torque is applied. For example, if a figure skater pulls in their arms, their moment of inertia decreases, and their angular velocity increases to conserve angular momentum, making them spin faster.

## Can you provide a real-life example of conservation of angular momentum?

A classic example of conservation of angular momentum is a spinning ice skater. When the skater pulls their arms in, they reduce their moment of inertia. Since no external torque is acting on them, their angular velocity must increase to conserve angular momentum, causing them to spin faster. Conversely, extending their arms increases the moment of inertia and decreases the angular velocity, slowing the spin.

## What role does external torque play in the conservation of angular momentum?

External torque is a force that can change the angular momentum of a system. If an external torque acts on a system, it can cause a change in the angular momentum. The conservation of angular momentum only holds true in the absence of external torques. When external torques are present, the change in angular momentum is equal to the applied torque multiplied by the time it acts.

## How do you calculate angular momentum in a system?

Angular momentum (L) in a system can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. For a point mass, angular momentum can also be calculated using L = r × p, where r is the position vector and p is the linear momentum. The cross product ensures that the angular momentum vector is perpendicular to the plane formed by the position and momentum vectors.

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