# Why Does Angular Momentum Stay Constant for a Spinning Ice Skater?

• xXhumans0monstersXx
In summary: This is the angular momentum of the skater. If the point of contact is at the same displacement but from the reference axis in the opposite direction, then the angular momentum is zero, because F(t)=-\vec F. So the angular momentum stays constant if the arms are pulled in closer to the body.
xXhumans0monstersXx
So basically, I was doing my AP Physics 1 homework and came across the spinning ice skater question yet again.

The question states, "An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?"

I already know that the kinetic energy increases, but can someone please explain to me why the angular momentum stays constant? I've done my research and I can't seem to find an explanation that I understand. I'm not the brightest when it comes to physics so if anyone could help that would be great! I have my first AP exam next week so a reply ASAP would be most appreciated. :)

xXhumans0monstersXx said:
So basically, I was doing my AP Physics 1 homework and came across the spinning ice skater question yet again.

The question states, "An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?"

I already know that the kinetic energy increases, but can someone please explain to me why the angular momentum stays constant? I've done my research and I can't seem to find an explanation that I understand. I'm not the brightest when it comes to physics so if anyone could help that would be great! I have my first AP exam next week so a reply ASAP would be most appreciated. :)

You should study more about angular momentum, specifically, conservation of the same:

https://en.wikipedia.org/wiki/Angular_momentum

xXhumans0monstersXx said:
why the angular momentum stays constant? I've done my research and I can't seem to find an explanation
Let's start with linear momentum. When a force ##\vec F(t)## acts from body A on body B for a time the contribution to B's momentum is ##\int \vec F.dt##. By the law of action and reaction, B exerts force ##-\vec F(t)## on A, so alters its momentum by ##-\int \vec F.dt## Thus the combined momentum is constant.
We can use the same for angular momentum. If the point of contact is at displacement ##\vec r## from the reference axis then taking the cross product of that with F(t) yields the angular moment and, on integrating, the change in angular momentum.

## What is the "Spinning Ice Skater Question"?

The "Spinning Ice Skater Question" is a physics thought experiment that involves a spinning ice skater and conservation of angular momentum.

## What is conservation of angular momentum?

Conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant unless an external torque is applied.

## How does the spinning ice skater demonstrate conservation of angular momentum?

As the ice skater spins, they have a certain amount of angular momentum. When they bring their arms closer to their body, they decrease their moment of inertia, causing an increase in their angular velocity. This increase in angular velocity balances out the decrease in moment of inertia, resulting in the conservation of angular momentum.

## What would happen if the spinning ice skater changed their body position without changing their angular momentum?

If the skater changed their body position without changing their angular momentum, they would experience a change in their angular velocity. This is because the moment of inertia of their body would change, causing a change in their angular velocity to maintain conservation of angular momentum.

## How is the "Spinning Ice Skater Question" relevant to real-world applications?

The "Spinning Ice Skater Question" is relevant to many real-world applications, such as understanding the motion of planets and satellites in orbit, as well as the behavior of spinning objects in space. It is also applicable in sports, such as figure skating and gymnastics, where athletes use conservation of angular momentum to perform complex movements and maintain balance.

Replies
4
Views
1K
Replies
9
Views
2K
Replies
14
Views
2K
Replies
6
Views
2K
Replies
11
Views
2K
Replies
2
Views
5K
Replies
13
Views
2K
Replies
1
Views
2K
Replies
4
Views
818
Replies
20
Views
12K