Let’s kick off this article with a riddle – you ready?
A vehicle goes past a light pole. Yet it’s always at the same distance from the light pole. How is this possible?
Take a few moments and think about this.
Motion in everyday life
Now the best part of a riddle is the “Aha” moment, which, unfortunately, I may have already spoiled with the title of this article. Sorry!
But just in case you are wondering, here is the answer, the vehicle is making laps around the light pole. Therefore, it is always at the same distance from the light pole although, at any moment, it looks like it’s going past it.
It’s an interesting way to kick off this topic because when we think of motion, the first idea that comes to mind is the action of moving away or towards something. It’s quite a straightforward way of thinking (pun intended). We’ve got our own experiences to blame for that.
- A ball is falling towards the ground.
- A car is headed towards the driveway.
- The rocket shot right up!
- Would you move that table forward?
These examples involve our common experiences with motion. But motion is much broader than just being linear. In fact, if motion was all one-dimensional, life wouldn’t be possible. Studying other kinds of motion helps us get a deeper understanding of how our universe works.
So let’s get to it!
Circular and Rotational Motion
These terms are mostly used interchangeably but there is a subtle difference between them.
Circular motion happens when an object goes around an axis (or another object). In more specific terms, a body in circular motion moves so that it traces a circle about the given axis. The body covers ground beneath it whilst simultaneously sweeping an angle about the axis.
The location of the axis is outside the body so we can imagine it as a particle going around an axis. Examples of circular motion include people in carousels or merry-go-rounds, or a car going around a roundabout.
On the other hand, a body in rotational motion rotates about an axis within the body. The particles that make up the body are in circular motion about the axis, but the body itself is not in circular motion.
A good example is a ceiling fan. The blades are in a circular motion about the centre, but the fan itself isn’t.
In everyday life, motion is usually a combination of linear and rotational motion. Your car, for example, utilizes the rotational motion of the wheels to create a linear motion of the car.
Pure rotational motion
They say all animals are equal, but some are more equal than others.
In the same sense, all rotating bodies undergo rotational motion, but some bodies are more rotational than others. For example, a rotating ceiling and swirling water in glass are both rotational motions. But one of them is a pure rotational motion and another is not.
Do you know which one is which?
Let’s take a closer look at the two rotational motions.
| Rotating Ceiling Fan | Swirling Water in a Glass |
| It’s rigid. The shape remains the same even if the changes in speed. | It’s fluid. The shape of the water changes continuously. |
| All points on the blades trace circles whose centres coincide with the centre of the fan. | Since it’s fluid, different points on the surface of the water may have different axes of rotation. |
| At a given time, all points on the blade of the fan sweep out at the same angle about the axis. i.e. they all move at the same rotational speed. | Different points on the water’s surface may sweep out different angles about the axis. i.e. rotational speed may be different at several points. |
Clearly, it’s much easier to study and model a rotating ceiling fan. Water? Not so much.
The rotating ceiling follows what’s known as a pure rotational motion. A rotating body is in pure rotation if all the points at the same radius from the centre of rotation have the same velocity. In the case of the ceiling fan, this means that if one blade turns through an angle Δθ in a time interval Δt, then every other blade must also turn through Δθ in the same interval.
Task one:
Select which one of the rotation motions below is a pure motion and which one is not! Let me know your answer in the comment section below:
- Rotation of the Earth
- Hands of a clock
- Rotation of the sun
- A cyclone
Studying rotational motion
Now that we have a rough idea of rotational motion, let’s probe a bit further. For our own sanity and peace of mind, let’s just limit this discussion to pure rotational motion.
Think of a ceiling fan that is rotating so slowly that a few bugs land on its blades. A bug at the far end of the blade would be moving faster relative to the environment around it than a bug perching at the middle of the blade. Although both bugs are sitting on the same blade, each is moving at a different speed.
Meanwhile, the bug sitting at the centre doesn’t move. It’s just rotating.
This begs the question: what is the true speed of the fan?
The little bugs on the blades wouldn’t be able to agree on this question. This implies that we need to come up with a new way of measuring the speed and velocity of rotating bodies. The old formula of speed = distance/time wouldn’t do.
Rotational speed and velocity
Let’s start with the conventional way of calculating speed.
$$Speed= (Distance )/(Time )$$
Using the bugs-on-the-blades example from the previous discussion, we have the following.
$$Speed= (Circumference )/(Time )$$
Since the bugs are moving in circles.
$$Speed= (2πr )/(T )$$
Since
$$(2π )/(T )=constant$$
Then,
$$Speed α r$$
This equation clearly stipulates that speed increases as one moves away from the centre of the axis. But as we have seen, this measurement isn’t best suited for our needs because different points on the fan have different speeds.
We need a generalized, discrepancy-free way of measuring motion.
Rotational angular speed.
Another way of looking at the speed of a rotating body is by the angle it sweeps about the axis rather than the distance it covers around the axis.
Back to the bugs-on-a-blade thought experiment:
Although each bug goes around the axis at its own speed, it always remains on the same line connecting it to the centre of the axis. In other words, they remain on the same blade of the fan even though each bug is moving at a different speed around the centre.
This implies that they are all sweeping angles in equal intervals of time. The rate of this motion is angular speed or angular velocity and it’s the standard way of measuring the rate of rotational motion.
The next part of this series delves deeper into rotational motion variables.
Major takeaway: understanding the concept of rotational motion and circular motion. Feel free to reach out if you have further questions.
