Centroid, Incircle and Circumcircle-These 5 real life example and their explanation will surprise you

Hey friends!

Welcome to askIITians!

If you are pissed off studying Centroid, Incircle and Circumcircle and still don’t know the application of it in real life then you are at right place.

Take a deep breath as I tell you 5 real life examples of it and their explanations

Just to remind you before we jump-in…

1. Centroid indicates center of mass of a uniform solid. Stick a pivot at the centroid and the object will be in perfect balance.
2. Circumcenter is a point which is equidistant from all the vertices of a triangle
3. Incenter is center of circle inscribed inside a triangle

Ever been to amusement park?

Ever played see saw in parks when you were kids?

See saw is a perfect example of Centroid in 1-Dimension.

Explanation:

Ever wondered how missiles balance themselves in air after they are fired?

Explanation:

Ok let’s consider this figure, front part of missile is loaded with tons of RDX and explosives and rear part contains entire propulsion system with fuel tanks, motor etc. Missiles are designed in such a way that its center of mass remains more towards the rear part and as gradually fuel burns up the COM shifts towards the center of missile.

Initial missile position is like this, COM is more towards the rearer part and mass on the rear part is more.

Final position of missile is like this, front part is heavy as most fuel in the rear part is burnt up and COM shifts towards the front end.

Why is luggage compartment of tour bus located at the bottom and not on the roof?

Explanation:

Lower the centroid (or center of mass) of a system more stable the system will be.

For the same reason extra passengers are not allowed on the upper deck of a crowded double-decker bus.

Why do you think racing cars are build low and broad?

Again for the same reason, lower the centroid more stable the system will be.

Also with lower center of mass driver can take sharp turns at high speed also without risk of toppling.

Circumcircle

Assume you are a city planner and you have pulled funds from 3 cites Delhi, Noida and Gurgaon to start a recreational club. Now the question is at which place should I open this so that it is equidistant from all the three cities.
Explanation: Mark all the three cities on the map. Join them to get a triangle and find its circumcircle, because that’s the place which is equidistant from all the 3 cities.

Look at the wall clock in your room, are you sure it shows correct time?

If your answer is yes, that means the manufacturer of clock has used concept of incenter to make sure center of clock coincides exactly with the incenter of the triangle inside which the clock is inscribed.