What’s the physics of rotational force?



Also, why do you spin faster when you bring your arms in?

In: Physics

You have the same energy in the rotating object if it has a radius of x or 2x.

But remember, a larger radius has a higher velocity for the same angular change as a shorter radius. So in this case the energy isn’t changing, but the object has a shorter distance to travel per rotation, so the angular velocity increases. If you extend back out, there is a larger distance to cover with the same energy available, so angular velocity slows down.

Physics of rotation is an extremely broad topic (as in, multiple college level lectures).

For your specific question, the reason we spin faster when our arms come in is that the “amount” of rotation (the technical term is angular momentum) a body is experiencing doesn’t change on its own. Just like an object will keep moving in a straight line without speeding up or slowing down if nothing is pushing on it, an object that is spinning will keep spinning at the same rate unless you do something to it.

The trick is that, for rotation, the “amount” of rotation depends not just on how fast they are rotating, but on how far from the center of rotation the stuff is. When you move your arms in, stuff is now (on average) closer to the center of rotation than before. So everything has to speed up a bit to keep that total angular momentum constant.

Angular momentum is defined as *L* = *r* x *p*

Where *r* is the distance from the centre and *p* being the linear momentum. Note that this is a simple multiplication but rather a cross product which is a fancier multiplication that takes into account the 3D aspect of the system. It’s a bit more complicated than that but to keep this ELI5, let’s leave it as fancy multiply.

As to why things spin faster when the weight is closer to the centre of rotation. Well think of it this way, the weight travels less distance. So in a sense, it’s “easier” and the system can spin faster as the weight is more centralised.

’Rotational force’ is a little strange wording. Generally rotation will be created by any force which has a moment arm, which will give it a moment. The rotation such a moment can give to an object depends on the mass of that object and how far from the centre of gravity that mass is located. This is a reflected in what’s called the polar moment of inertia.

If no external moments are acting on a an object, that object’s angular momentum (which is dependent on angular velocity and the polar moment of inertia) will stay the same. So if you bring your arms in, your mass will be closer to your centre of gravity, so your polar moment of inertia will go down. Your angular momentum stays the same, so your angular velocity will increase (which means your start spinning faster).