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Lasha P.
Student of M.Sc in Physics
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Physics (Newtonian Mechanics)
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Question:

A disk of M mass and radius R makes rotation. Its angular velocity is $$\omega_0$$. Another disk with the same mass but r radius is dropped on top of the rotating disk, it its center. The new spinning system rotates with new angular velocity w. Assume, we do not have loss of the energy, what is w?

Lasha P.
Answer:

Angular momentum is conserved. Therefore, we should write initial and final angular momentum and make equality. For the initial case we have $$L_{i}~=~ I \omega_0$$ $$I$$ is the inertial moment which is $$MR^2/2$$ for the disk. After the second disk is dropped on the top of the first disk, inertial moment will be changed. After drop, total inertial moment $$I~=~M(R^2 + r^2)/2$$ . When we solve for the equality for angular velocity we will simply get: $$MR^2 \omega_0 ~=~M(R^2 + r^2) \omega$$ , $$\omega~=~ {R^2 \omega_0}/{R^2 + r^2}

Pre-Calculus
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Question:

Find the derivative of the function: $$f(x)~=~ ln(sin(2x))$$

Lasha P.
Answer:

$$\frac{df(x)}{dx} ~=~ \frac{2}{sin(2x)} cos(2x) $$ Here we have combination of three functions. Its derivation should be derived step by step. First, we write derivative on the logarithm, then sin and after argument of the sin.

Physics
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Question:

What is physics?

Lasha P.
Answer:

Physics is a phenomena that we interact everyday. Sometimes students think that physics are formulas and tedious algebra that they meet during solving the problems. From there point of view, it is some distant cluster that rarely intervenes in our life. However, they are mislead. We cannot even read this question&answer without optics, that is one of the fields in physics. Learning this subject helps one to deeply understand way of processes that happens in life. There are a myriad of analogies in life that can be interpreted as a physical problems. Consequently, physics is a everyday life.

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