D. Indumathi, The Institute of Mathematical Sciences
You must have often seen little children holding a colorful wheel on a stick and running down the road. The wheel rotates in the wind.
If you stare at a wheel spinning in front of you, you will observe that it is rotating uniformly. That is, every point on the surface of the wheel seems to flash past your eyes at the same speed. This is clearly seen in a slowly rotating fan: the blades all move at the same speed about the centre of the fan. If you are exactly below (or in front of) the fan, the blades also uniformly rotate past your eyes. This happen because the centre of the fan is not rotating; it is fixed with respect to you. Hence the constant speed of rotation about the centre of the fan is also seen by you as a uniform smooth rotation.
What happens when the centre of the rotating object is also moving, say, away from you? This is the case with a cycle or car wheel: the wheel is rotating about a central point, but this central point is itself moving, since the vehicle as a whole is moving. So there is two types of motion that the wheel is taking part in: rotating about its centre and linear motion of the wheel as a whole.
A simple experiment will show you how a typical point on the surface of the wheel moves.
Take a large plate and mark off four points North, East, West and South, as shown in the picture. Highlight one of the points (say, North) by making it bigger or circling it. Also mark off the intermediate points North East, South East, South West and North West.
Now we have a round plate with 8 equidistant points, one (North) distinguished. Hold the plate up against a wall with North on top. South is touching the ground (see the picture on the next page). With a pencil, lightly mark the position of North on the wall.
Rotate the plate forwards so that the next marked point (South West or South East) touches the ground. Again mark the position of North on the wall.
Keep rotating the plate and marking the position of North. Continue until you have at least a dozen points marked on the wall. Take away the plate and see what kind of pattern you have made on the wall. Was it something you expected? What do the dots tell you about the manner in which a point on the plate (which is our model for a wheel) moves?
Abhijit Deshpande, IIT madras, Chennai
You would have obtained a pattern which looks like the picture below. As the plate or “wheel” rotates, it moves forwards. You can see that when a point on the wheel (North, in our experiment) is on top (positions 0 & 8), its moves forwards a greater distance (0 to 1, 8-9) than when it is near the ground (4-5).
What does this mean in terms of the speed of the point? In our experiment, we rotated the “wheel” (plate) by equal angles at a time (45 degrees, actually). If the vehicle on which the wheel is was moving at a constant speed, every such turn happens in equal intervals of time. We know that speed – or rather, let us use the technical term, velocity- is nothing but distance moved in a given time, divided by that time. Since the points we have marked out are not equidistant, the (forward) velocity of a point on a wheel changes as it moves from top to bottom. Or, different points on a rotating wheel have different velocities! But remember that all points on the wheel are rotating with the same (angular) velocity around the centre of the wheel. They appear to move with different speeds for a person standing and watching the wheel. This happens because the wheel is not just rotating about its centre; it is moving on the road too. Contrast this with a fan.
Since the centre of the fan is fixed with respect to us, the blades of the fan appear to move uniformly. Let us get back to our plate. Can we approximately tell what is the variation in the speed of a point? Measure how much the plate has moved forward in eight turns (the point North going from top to bottom back to the top). Suppose it is 8 cm. The average velocity of the point is 8cm in eight units of time, or 1 cm per unit time. Notice that the point North moves from position 7 to 9 in two units of time. That is about 4cm, about twice as fast as the average velocity. Whereas from position 3 to position 5, North hardly moves at all. If you can handle a little algebra, you can work out that a point on top of the wheel has twice the average velocity, whereas a point at the bottom has zero velocity. Points in between having continuously changing velocities between these two extremes. So next time you see a bus going past, think about the fact that the points at the bottom of the wheel are taking an instantaneous rest while the bus as a whole is moving. It’s true!
Cut open a balloon to get a fairly flat piece of rubber. Cover a glass jar or bottle with the balloon piece and tie it tightly with a rubber band or piece of string. (If the mouth of the jar is small enough, you can just stretch a whole balloon tightly over the mouth). Grip the balloon firmly at the centre with your fingers, raise it, and let it go. You will hear a pop sound. A pop-up sound is usually heard when the air pressure is equalized suddenly across two sides of a surface. In this case, when you pull the balloon, the air that was inside the bottle gets redistributed uniformly over a large volume, leading to a partial vacuum. Hence there is greater air pressure outside than inside. When you let go, the sudden release of the balloon compresses the air inside, and the resulting equalization of pressure causes a pop sound to be heard. A drum makes sound in the same way.
A membrane is usually tied tightly over a frame, and beaten with a stick or the hands. When the drum is beaten, the air inside is suddenly compressed, leading to a pop sound. The same principle is what makes our ears go pop every once in a while. As you are reading this article, you can make your ears pop by simply swallowing. (Try it!)
The periodic popping is very necessary to protect the sensitive ear-drum inside our ears (see the next page for a picture). It is in fact the middle ear that plays a role in this popping activity. The ear is not an independent organ; it is connected to both the nose and throat because of the Eustachian tube which connects the middle ear to the nose. The Eustachian tube is lined with a membrane (similar to the one in the nose) that continually absorbs air.
Hence the amount of air in the middle ear decreases, leading to an air pocket inside the ear just as in our experiment. When we swallow food (or even just saliva), a small amount of air enters the Eustachian tube from the nose and enters the middle ear, equalizing the inside and outside pressure. This results in a popping sound. Hence the air that is absorbed in the middle ear is continually replenished during swallowing If for some reason (for example, when you have a cold) your nose is blocked, the air cannot enter the Eustachian tube from the nose and hence there is a difference of pressure between inside of the ear and the outside. This pressure difference causes the ear to feel blocked. The relative vacuum inside makes the eardrum get sucked inwards.
Hence it is not able to freely vibrate, impairing normal hearing. If the nose block is severe, the ear drum gets painfully stretched and is the cause of severe discomfort. This is a temporary discomfort that disappears with the cold. But occasionally, fluid may start to ooze out from the membranes in an attempt to fill the middle ear cavity and equalize the air pressure. This may also be due to various nose or ear infections. Discomfort due to such pressure differences on the ear can be felt during air travel, especially during landing, when the aircraft is moving from the low atmospheric pressure high up to the ground. Air pressure inside the aircraft cabin is controlled, but not completely.
The eardrums stretch outwards during take off and inwards during landing (can you say why?). Popping your by swallowing eases the discomfort during landing, when the increasing air pressure causes the vacuum to form faster than normal. Can you think of other situations when your ears hurt due to sudden changes in pressure?
Question to think about: When you blow your nose, it is recommended that you blow one nostril at a time (that is, close only one nostril at a time). Why? Parts of the ear The ear is divided into three parts, the outer, middle and inner. The outer ear includes the pinna, as well as the ear canal which you can see disappearing into the side of your head. The canal ends in the eardrum, which vibrates when any sound waves are channeled into the ear by the outer ear down the ear canal.
The vibrations of the eardrum are transferred to three small bones in the middle ear, which in turn pass them on to the nerves in the inner ear. These vibrations are picked up by the nerves and transmitted as nerve impulses to the brain. The brain decides whether you are listening to the wailing of the next door neighbour’s baby or Beethoven’s 9th symphony.
The inner ear also affects your sense of balance (when you twirl around, you feel dizzy).
Source: The American Academy of Otolaryngology
Abhijit Deshpande, IIT-Madras, ChennaiDo you remember the last time last time you tried to get tomato ketchup from the bottle? Did it happen that no matter how hard you shook the bottle, the ketchup refused to come out! In such a case, what might have worked is tilting the bottle up and trying to pour it again. Or inserting the back end of a spoon and making the ketchup flow.
Abhijit Deshpande, IIT-Madras, ChennaiWhat is the most important component of rice? Starch, of course. We eat rice so that we get a good supply of starch. This starch is taken up in our body and digested. This digestion process gives us energy to do all the different things we do. Is it possible for us to buy starch by itself? Yes, if you go to a grocery store, you can buy cornstarch. Whenever soup is made in your home, cornstarch may be used. It is used while cooking soup because it makes the soup very thick.
Source: Portal Content team
Last Modified : 3/2/2020