Recent content by Aleoa

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

You are right. My misunderstanding started because i can't properly understand what is the same dv that A and C get according to the force law \bar{F}=m\frac{d\bar{v}}{dt} that applies equally in both points

Let's only consider the points A and C. Since the gravitational force is the same in both points, in a dt they get the same dv and so a different d\omega =Rdv. Is this correct ?

Let's get back to my first question. If i can replace the objects in A and C with the two objects in B, in a dt what is the infinitesimal quantity that they change in the same way?

Yes, however, I don't understand what is the property of the triangle inscribed in a semicircle that allows me to prove that ##t_{AB} < t_{ACB}##

Then why the author says that the 6 blocks highlighted in grey have the same effect as a single block in A? Can you explain to me more deeply?

I'm really sorry, but i don't understand how to solve this problem. Can you give me some help ? This is the picture of the problem:

I'm trying to derive the lever law by myself, however, I'm stuck. Please follow the logic of my calculations. Every object in the picture has the same mass. I want to prove that, under the effect of the gravitational force, I can replace the objects in A and C with the two objects in B, and...

This means that Fdl is a very important quantity, i suspect it's a conservative quantity. How can i analyze Fdl matematically (or physically) just to understand what means that it's a conservative quantity ? The fact that the integral of Fdl has the name "work" say nothing to me, they could...

When we write \int m\frac{d\bar{v}}{dt}d\bar{l} , what is the physical meaning of weighting the m\frac{d\bar{v}}{dt} with the dl ?

So what is the fundamental quantity we are summing using the integral ? Doing some calculation I get the basic quantity we sum is mvdv, but physically what this quantity represents? It seems so an arbitrary quantity to me...

My intuition is that in the integral formula of the work \int m\frac{d\bar{v}}{dt}d\bar{l} the vectors dt and dl are linked, and that the integral simply represents the sum of all the mdv / dt along a path. Is this true ? How dl and dt vectors are linked ?

I want to understand very deeply the meaning of the work integral formula: \int m\frac{d\bar{v}}{dt}d\bar{l} It is not enough for me to know that it was defined in this way, I want to know why it was defined in this way. To start, what is the physical meaning of m\frac{d\bar{v}}{dt}d\bar{l}...

I want to model a sensor with the static behavior: y(t)=a+by_{0}(t) using a first order lag: G(s)=\frac{K}{1+Ts} However, if i try to convert this order lag in time domain and set the derivative as 0, what i get as static response is: y(t)=Ky_{0}(t)=by_{0}(t) And the a constant has...

Months have passed and I could not create the model. Is anyone kind enough to show me a possible solution?