I came across a question on Quora that asked to explain angular momentum in “layman’s terms”. Whenever someone asks me to explain a physics concept in simple terms (or in this case “layman’s terms”) I feel incredibly challenged. I am immediately reminded of Albert Einstein’s famous quote if you can’t explain it simply, then you don’t understand it well enough.
So here is the objective of this article: to explain angular momentum simply.
Whether this objective will be accomplished or not, you’ll be the judge of that!
So, without further adieu, I bring to you “angular momentum in layman’s terms”!
For starters, I would first define angular momentum informally as a property of a body in rotational motion.1.
Later we will get in-depth and dissect this property in detail. But for now, let’s keep it like that.
This particular property (that we now call angular momentum) is exclusive to bodies that are rotating. When an object stops rotating, it loses this property.2.
Angular momentum like money
Angular momentum is something a body has, like money.
This also means a rotating body can gain, lose or maintain its angular momentum. Just as you can gain, lose or keep (maintain) your money.
When you work, you earn money. Likewise, when an object rotates, it “earns” angular momentum – simply by virtue of its rotational motion.
When you stop working, you stop earning money, likewise, when an object stops rotating; it stops having angular momentum. In addition, when an object is rotating very fast, it has a bigger angular momentum. Just like when you are working really hard, you (ideally) earn more money. and vice-versa.
In the absence of external influences, the angular momentum of an object is conserved. Just as how your money is conserved in the absence of expenses such as when you securely hide it in a safe, or a bank.
Disclaimer: In this article, angular momentum is likened to money for clarity reasons only. I recommend you read this article with a healthy bit of skepticism because angular momentum is not money. And there are many ways that money fails to relate to angular momentum. For example, we just said that angular momentum is conserved in the absence of external forces (more on this later). And we likened that to how money is also conserved in the absence of expenses. In reality, though, money can depreciate over time. This means the value of money that you have may decrease with time even when you lock it away in a bank or safe. Angular momentum on the other hand is not subject to inflation or depreciation.
Angular Momentum: Going deeper
Now, this is the part where we dive deeper into this “property” that we’ve called angular momentum. Keep in mind this is a layman account of angular momentum so there might be “a little more to it than that”. Reader skepticism is advised!
All rotating bodies have angular momentum, but as just as George Orwell proclaimed in his famous political satire Animal Farm, “All animals are equal, but some animals are more equal than others”.
We could state a somewhat similar statement, “All rotating objects have angular momentum, but some objects have more angular momentum than others”.
Think of it this way:
A person earns money by either working very hard (similar to a body rotating very fast) or by doing a more difficult task (similar to the difficulty of a body to rotate).
“People are paid in proportion to how hard they work, and how difficult their job is to do”
Similarly, “bodies acquire angular momentum in proportion to how fast they rotate, and how difficult it is to rotate them”.
Thus, the blades of a rotating helicopter would have a bigger angular momentum than say, the blades of a rotating ceiling fan, even though both may be rotating at the same angular velocity. This is because the latter is much more difficult to spin.
The angular momentum of a rotating body depends on its speed of rotation (called angular velocity), and its difficulty to rotate (called rotational inertia).
I hope I made sense here because the next part builds on this.
Calculating angular momentum
Following up on our previous discussion, we could loosely state the following mathematical relation,
Earnings (Money) = Hard work x Work difficulty.
This equation simply means that the amount of money you potentially earn from a job is a product of your hard work and the difficulty of the job.
Note: By difficulty of a job, I don’t mean the amount of sweat you crack while carrying out the task but rather how society regards the job as difficult. Clearly, a janitor cracks more sweat doing his job than the accountant sitting behind a desk the whole day. However, a janitor is paid far less than an accountant is because society perceives the janitor’s job as easy. The janitor’s job isn’t difficult to learn and he/she can be replaced by anybody, unlike the accountant who spent years learning numbers, and saves clients thousands on their taxes on a daily basis.
Okay, I digress. But this point still stands:
“People are paid in proportion to how hard they work, and how difficult their job is to do”.
If you work very hard on a job that is generally perceived as easy, you won’t be paid as much. And vice-versa.
Unlike earnings of a salary, angular momentum is literally the product of angular velocity and the rotational inertia of a rotating body. Mathematically, we write
Angular momentum = Rotational Inertia x Angular velocity
Or symbolically
L = Iω
The SI unit of angular momentum is kgm2/s.
Here angular velocity (the speed of rotation) and rotational inertia (the difficulty of rotation) both contribute to the angular momentum of the rotating body.
This implies we can actually represent the angular momentum of a rotating object with a number and a unit. That number is called “the magnitude of angular momentum”.
Angular momentum has a sense of direction in space.
In addition to having a magnitude of a certain unit, angular momentum has a sense of direction in space.
It may (also, quite literally) point up, down, left, right, or anywhere in between. This is important: without direction, this property is practically useless. This is because angular momentum is a vector quantity; that is, it is specified by magnitude as well as direction.
Read: What is a vector.
Think of it this way:
You can be working really hard, and doing a very difficult job, but if your work lacks objectivity, then it’s pointless and you won’t earn any money.
Counting the sand of a seashore is a hard and difficult job to do, but you are unlikely to earn anything from it because it lacks objectivity. Working hard or doing a very difficult job doesn’t mean much if it doesn’t have a sense of “direction”.
It’s a flawed analogy, but you get the point.
Once when I was a kid, I tried to wash all the stones and pebbles in our compound. Phew! What a waste of time and effort that was!
Anyway, working hard or doing a very difficult job doesn’t mean much if it doesn’t have a sense of “direction”.
Likewise, this property called angular momentum cannot be fully specified unless it has some sense of direction. This sense of direction is related to how the rotating object is oriented in space. A table fan that rotates facing north and another table fan rotating facing south have different directions of angular momentum because their orientations are different.
Angular momentum requires both magnitude and direction to be completely specified
Conservation of angular momentum
This is probably the most interesting and important aspect of this property.
When a body is rotating in the absence of external influences from its environment, its angular momentum will remain the same in both magnitude and direction. This is the law of conservation of angular momentum.
This might seem like a simple statement but it has profound implications in physics.
Remember we defined angular momentum as the product of rotational inertia and angular velocity,
That is angular momentum = angular velocity x rotational inertia.
If angular momentum is to be conserved, then any change in the rotational inertia of the body must immediately be compensated by a change in the angular velocity of the rotating body in order to balance angular momentum. And vice-versa.
If we refer back to our social analogy,
Salary = hard work x difficulty of work.
Then for you to maintain your salary, you either have to pick up a more difficult job and work less hard, or pick a less difficult job and work yourself out. Either way, your salary will be unaffected although you may now be working less hard (but on a more difficult task) than before.
I could revisit the janitor/accountant example once again, but you can probably relate this on your own.
A spinning ice-skater and angular momentum
There are many examples of the conservation of angular momentum in real life, but we will consider only one here: a spinning skater.
As any skater can testify, it is much easier to spin when you pull your body together than when you extend your arms outwards, the little GIF demonstrates that.
While in the air, she pulls her arms close to her body while spinning, in doing so, she lowers her rotational inertia and consequently, she spins faster. This enables her to do several spins in mid-air. When she lands back on Earth, she extends her arms outwards, in doing so; she increases her rotational inertia and consequently spins much slower than before.
In either case, her angular momentum ( = angular velocity x rotational inertia) remained the same even though her rotational inertia and angular velocity were changing.
Another way of expressing conservation of angular momentum is,
Angular momentum before = Angular momentum after
Angular momentum is transferable
This follows directly from the fact that this property is conserved. Angular momentum can be transferred from one body to another.
When you have a system of isolated bodies .i.e. bodies that can interact with each other without influences from the environment, then this property may be transferred from one body to another while the total property of the system remains constant.
Okay, this pretty much sums my layman explanation of angular momentum. To cap it off here are some everyday observations that angular momentum can explain.
- The wobbling of your ceiling fan
- The stability of a moving bicycle or a spinning top. Ever wonder why a moving bicycle is much more stable than a stationary one. Someone even famously said, “Life is like a bicycle, to maintain your balance you’ve got to keep moving”. Very few actually know its “something to do with” angular momentum!
- The strange behavior of a rotating gyroscope. No one is too old to have a toy gyroscope trust me!
- Why a helicopter has two rotors. True, a single rotor would be a less interesting design, but again, as they say, “there’s more to it than that”!
- Ever wondered why the Earth rotates at all?
And so much more…
Honestly, I would’ve loved to explain all of these situations in detail, but one can only read much in a given time. I have linked out to other websites that I believe have the best descriptive explanations for those scenarios. These are secondary sites not connected with this one and I take no responsibility for their content.
What then is angular momentum?
At the beginning of this article, we defined angular momentum informally as a property of a body in rotational motion.
As for the formal definition of angular momentum, here is one from Merriam Webster Dictionary.
Angular momentum is a vector quantity that is a measure of the rotational momentum of a rotating body or system, that is equal in classical physics to the product of the angular velocity of the body or system and its moment of inertia with respect to the rotation axis, and that is directed along the rotation axis.
Can’t see why we didn’t just lead with this.
Thank you for reading and come back for more!
