In everyday life, when we have to walk, run, cycle, drive or fly round a bend or a circle, it always feel a bit different from going in a straight line. If I just want to turn a bit to the left when walking, may not feel so obvious that I walk any differently. But if I do it quite fast, I would feel that my right leg is pushing harder on the ground than my left leg. That helps me to move to the left. What I keep on doing that? Then after moving left a bit, I move left a bit more, and a bit more ... I start going round in a circle ! So it seems that in order to move in a circle, there has to be a force sideways - at right angle to the original direction.
In everyday life, we sometimes have to talk about angles. Like when we rotate something, or talk about some directions. Most people probably knows what 90 degrees, 180 degrees and 360 degrees mean.
Just as there are more than one type of units for length - like kilometres and miles - so there are other types of units to measure angle, like radian and gradian.
Degree is probably the most commonly used. I have never heard of gradian. A google search brings up its Wikipedia page, which explains that 1 gradian is 1% of of a right angle.
That is to say - 100 gradian is equal to 90 degrees. It is used in certain professions like surveying and, guess what - in HTML and CSS for webpage design! Apparently, people find it easier to think of 1 part in 100 rather than 1 part in 90 of a right angle.
Come to think of it - can you imagine if instead of using "100%" to mean everything, we use "90%" ? But that is exactly what we normally do when we call the right angle 90 degrees!
In life, we get use to things that we live with. By secondary or high school, we get used to calling a right angle 90 degrees, and the complete all round angle 360 degrees. Just when we think we know all about angles, we have to learn a new unit for angle when I study physics - radian. In the beginning, learning using "radian" can be even more confusing than using the gradian unit mentioned above. 360 degrees is 2π radians. π is a Greek letter, pronounced "pie" in English. π is approximately equal to 3.1416. Radian is yet another unit of angle. 1 radian is equal to 57.30 degrees. Mind boggling.
But as it turns out, if we use radian as the unit for measuring angle, the formula to calculate distance and speed of an object going round in circle becomes quite simple. It goes like this
speed = radius x rotational speed (in number of radians per second)
I shall not show what it looks like if we use degrees, but it basically requires multiplying the radians by a formula to convert degrees to radians.
Although it takes some time, it is possible for students to get used to radians after some practice. What gives students a hard time is actually the force that is needed to have a circular motion.
We all know what a force is, right? If I push an object with a force, it will move in a straight line, as long as my force is more than the friction. To make things simple, lets take it there there is no friction.
If I want the object to move in one direction, my force has to be in that direction. Obviously, right?
Now what if I want the object to move in a circle instead. I cannot just push in the same direction all the time - it would just go straight. Obviously, I have to keep changing the direction of my force.
Here comes the tricky bit - after pushing straight for a bit until the object has the speed I want, I have to start pushing sideways instead to make go in a circle !
If you think about it this way, it may start to make sense.
But how do we understand the fact that even if an object is moving round a circle with the same speed round and round, it is actually accelerating ?
There are two ways for us to convince ourselves about this.
1. There must be a force to keep pulling the object sideways, at right angle to its direction. If this force is not there, the object would just go straight.
2. The direction of the object keeps changing in the circle. That means the velocity keeps changing. So it has acceleration.
This is where we have to get used to the fact that acceleration happens where whenever there is a change in velocity. Since the meaning of velocity includes both speed and direction, there is acceleration even of an objection is moving in the same speed round a circle - since the direction is changing.
So acceleration is not just about going faster and faster, a meaning we are used to in everyday life. In physics, we have to get used to the vert strict meaning of acceleration:
When there is any change in velocity even if it is just a change in direction without any increase in speed - then it is considered an acceleration. This is thinking about the meaning in a very very strict sense - something that many students may not realise they have to do when they study physics.
You can learn these concepts and more at Dr Hock's maths and physics tuition.