Anmol is Blogging

If there was no friction, then one could keep a nut on one end of a screw and it would automatically screw/roll-down/tighten itself if kept in right orientation under the the influence of gravity.

A few days ago, me and a friend of mine challenged each other to see if we could mathematically prove that the acceleration vector always points radially inward for a body in circular motion. So here's what I came up with: Proof We know the position vector for a body making an angle \(\theta_0\) with the X-axis is given by: \begin{align*} \vec{r}=r\,(\cos{(\theta_0)}\,\hat{i}+\sin{(\theta_0)}\,\hat{j}) \\ \end{align*} But for a body revolving around the origin, the angle changes at the rate \(\omega\). That is to say: \begin{align*} \omega=\frac{d\theta}{dt} \\ \end{align*} So in general, the angle at any given time \(t\) would be (\(\theta_0+\omega t\)). Which implies the position vector would be: \begin{align*} \vec{r}=r\,(\cos{(\theta_0+\omega t)}\,\hat{i}+\sin{(\theta_0+\omega t)}\,\hat{j}) \\ \end{align*} Now since we have the position as a function of time, we can take the its derivative w.r.t. time to get the velocity function. \begi...

Some simple sequence of arguments can be made to see how the statement contradicts itself. Statement 1: "Nothing is impossible." Which follows that everything is possible. So statement 1 can be re-written as: "Everything is possible."  For now, we assume that statement 1 is true. Now let us consider a new statement and call it statement 2 which says,  "Statement 1 is false." So is statement 2 true? Well, according to statement 1, everything is possible; therefore it must be  somehow  possible to proof statement 2. But if statement 2 is true, then statement 1 is false. Or another way to put it is that statement 1 is NOT true if it is true. And we clearly see the contradiction here !!! Conclusion: "Nothing is impossible" is impossible!   😉

I remember the date very clearly, it was November 26, 2021 when I experienced sleep paralysis  for the first and hopefully the last time. I'm not entirely sure but I think it happened because of me messing with my sleep schedule. I was very inconsistent with my sleep cycle. On some days, I'd go to sleep at 10 in the night and on others, it would be 3 in the morning. So... yeah, I was totally chaotic. I've been a lot more consistent with my sleeping schedule ever since I experienced sleep paralysis. That definitely taught me a lesson 😂. I had decided to sleep early that day. I was on my bed in my room with the doors closed from inside. I guess it was somewhere between 2 to 3 A.M on November 26 when it happened. My eyes randomly opened and all I could see was my dark room with light coming from the windows. I tried to move my body and shift my position on bed but I found myself unable to do so. I was constantly trying but it seemed like I had lost control over my muscles. I ...

Almost two years ago, I was performing an experiment. The goal was to use a transformer and a variac to achieve a visible electric arc. I also used a digital multimeter to measure the voltage (with a maximum AC voltage rating of 750v). So, the plan was to connect the output of the variac to the secondary coil of the step-down transformer (which made it function as a step-up transformer); its primary coil terminals was the output of the system and was hooked-up to the multimeter. According to the plan, I used the variac to increase the voltage from 0v to 240v which was further multiplied 20 times using the transformer and whose output was measured using the multimeter. Since the max. AC voltage rating was 750v, I thought it could very easily tolerate upto 650v after which I would have disconnected the multimeter from the whole system. And continue raising the voltage. I was nervous and excited at the same time. I flicked the switch and started the experiment. Everything was normal as pl...