## Lower Part of a Wheel Travels Slower

###### By Anupum Pant

Stick a colourful piece of paper on the side of a rim of a wheel and make the wheel roll away. If you observe carefully you’ll see, whenever the paper is near the ground, it appears clearly. However when the paper is at the top of the wheel, furthest from the ground, the paper appears hazy.

Also if you observe the spokes of a wheel of a moving cart, you’ll see that the spokes at the lower part of the wheel appear clearly. While the spokes of the upper part appear to blend into a single body, as if travelling much faster than the lower part.

It seems, the upper part of the wheel is travelling at a higher speed than the lower part of the wheel. How can that be, when both are physical extensions of a single object?

Yes, in fact the upper part does travel faster than the lower part. This sounds incredible, while it seems very ordinary to others who understand the simple physics of it. The physics involved really is very basic. So basic that I’m sure many reading this are cursing me for writing something so ordinary. But I find it really incredible. And believe me, there still are people who need to know this.

Let’s suppose the wheel moves at a speed of v in the right direction. However that is just the speed of the centre of the wheel. The upper part of the wheel for instance rotates at a speed of, say v, and also translates in the same direction at a speed of v. So, the speeds add up. And the top is travelling at a speed of 2v.

Similarly, at the bottom part of the wheel, the rotation is in the opposite direction (towards the left) and translation is in the right direction. Hence the speeds get cancelled and the lowest part of the wheel is stationary.

These are the topmost and bottommost points I’ve discussed here. For all the other points on the rim the rotational speed v gets split into a horizontal and a vertical component. So their speeds vary and lie in between 0 and 2v.

Some call it the cartwheel riddle.

Now, if you already knew that there’s something mind-boggling for you here. There’s another similar thing about wheels which blows my mind. Demonstrated in the video below…

## Train Wheels are Not as Simple as They Seem

###### By Anupum Pant

I’m pretty sure not many of you know this about train wheels, neither did I.

Look at the picture and answer this: What do you think keeps a train moving on the track? or Which part of the wheel do you think it is that keeps the train from careening away from the track at turns?
Applying general logic, I thought that flanges at the end of the wheels  kept a train from going off rails at a turn. Turns out, I was wrong!

In fact, flanges at the end of the wheels are just a safety mechanism to keep the train on its track only if the main mechanism fails. And what is that main mechanism?

Train wheels are conical in shape. That means they have a varying diameter at different points of contact. Now, suppose the track turns right. The train’s left wheels now have to travel more than the right wheels because at the turn the track on the left is longer.

So how do the left wheels travels more than the right wheels without a differential?
Since the wheels are conical in shape, the whole wheel-set shifts a bit to the left, if the track curves right. Now the point of contact of the left wheel is at a larger diameter of the cone. While the smaller wheel touches at a point where the diameter of the wheel is lesser. Therefore, if the left wheel now makes one circle it travels further than the right wheels and the train moves along the curve smoothly.

The whole beauty of this system is that the amount of shift of the wheel-set happens automatically, makes the train move on turns smoothly and keeps the train on track.

Look at how you can try this at home using 2 plastic cups and 2 similar pipes. [Experiment]

If I couldn’t explain it properly, probably the best physics teacher ever – Richard Feynman – will explain it to you better. [Video]