# Tutor profile: Mahindra R.

## Questions

### Subject: Physics (Newtonian Mechanics)

Why do Boomerangs Come Back?

Boomerangs work on the same principles of aerodynamics as any other flying object; the key to how a boomerang works is the airfoil. An airfoil is flat on one side but curved on the other with one edge thicker than the other - this subjects the boomerang to lift, keeping it in the air. The lift is generated because the air flowing up over the curve of the wing has further to travel than the air flowing past the flat side. The air moving over the curve travels faster in order to reach the other side of the wing, creating lift. A boomerang has two airfoils, each facing in a different direction. This makes the aerodyamic forces acting on a thrown boomerang uneven. The section of the boomerang moving in the same direction as the direction of forward motion moves faster than the section moving in the opposite direction. Just like tank tracks moving at different speeds, this causes the boomerang to turn in the air and return to the thrower. Fast Fact: Most original boomerangs don't come back, and are not intended to do so! The returning variety are thought to have been made to scare birds into hunters nets.

### Subject: Basic Math

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Explanation: Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9/20.

### Subject: Aerospace Engineering

How to design a structural component for vibration ?

In order to design a structural component for vibration, first, we should know its steady-state response under external harmonic excitations. In real life, accelerometer provides these data. The time domain data can be converted into the frequency domain by using fast Fourier transform. The frequency at which the peaks are coming in FFT are the natural frequencies of the structures and since it is matching with the external excitations, causing it to have resonances. At resonances, displacements shoot up, which we don't want. Now we know the range of external excitations, we have to design the structure in such a way that natural frequencies should not fall in this range. This can be done by modifying the material property, shape, boundary conditions and mass of the structure. The magnitude of the loading is not a major concern but the frequency of the loading is the concern.

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