Angular Momentum
Angular Momentum: What Is It?
Let’s start with the basics. First of all, What is momentum?
In order to understand momentum, we must first look at Newton’s Three Laws of Motion.
1st: A body in motion or at rest, will remain that way unless acted upon by some external force.
EX. Someone who is sliding on ice would continue to slide unless some force, like friction or a strong wind, were to stop them.
2nd: F = m*a, in other words, force is equal to an objects mass multiplied by its acceleration (acceleration is how fast something is speeding up or slowing down).
EX. If you were pushing your lawn mower across your yard, you are exerting force on the lawn mower, which has a given mass. That force applied to the lawn mower causes it to accelerate.
3rd: For every action, there is an equal and opposite reaction.
EX. If you are sitting in a chair, you aren’t only pushing down on the chair but the chair is pushing back up on you (otherwise you would fall to the ground if the chair wasn’t pushing back).
Now that we have defined these terms, let’s talk about the conservation of momentum. Momentum conservation depends on Newton’s 2nd and 3rd Laws. Since acceleration is equal to the change of velocity divided by the change time:
F = m * (v2 – v1)/(t2 – t1) (1)
This can be rearranged to:
F * (t2 – t1) = m * (v2 – v1) (2)
The mass times the velocity is the momentum of this system. Note that if the change in time (t2 – t1) is approximately zero, then there is no change in
momentum. Thus, momentum is conserved!!!
Now let’s look at an object that is moving in a circular path. We can now introduce the concept of angular momentum, which is given by
L = r * m * v (3)
where r is the radius, m is the mass of the object, and v is its velocity.
Just like linear momentum, which we defined above, angular momentum is always conserved too!! So now let’s look at an example.
Let’s say that you have a rock tied to a string and you are spinning that rock in a circular motion around your head. If you know the mass of the rock, the length of the string between your hand and the rock, and how fast the rock is moving in that circle (the angular velocity), then you can calculate the momentum from equation (3).
Now, if you shortened the length of the string, and the mass of the rock stays the same, and you wanted to conserve angular momentum, then the velocity has to increase.