# Tag Info

Accepted

### Is radians a dimensionless quantity?

radian is a derived unit, defined as the ratio of arc length to radius. As the ratio of two lengths it is dimensionless.
• 949

### Determine the moment of inertia of a filled circular sector

Consider an infinitesimal element of area $r d\theta dr$ which is at a distance $r \sin (\theta)$ from the $x$ axis. Its moment of inertia is $r d\theta dr (r \sin (\theta ))^2$. The moment of ...
• 1,971

### Variation of LED light as a function of distance

All EM radiation from a point source falls off in intensity with the square of the distance. LEDs can't magically change this basic physics. LEDs can be quite directional in their emission pattern. ...
• 11.4k
Accepted

### Does every engineering design needs to have a complete theoretical backing or may experimental data suffice?

Are any designs based solely on data from trial and error used in critical mainstream engineering? Usually not. And the reason is that trial and error is expensive and time consuming. As engineers, ...
• 2,646
Accepted

• 238

### Matrix Calculation

Your numbers are right. You are just confused about matrix multiplication. See https://en.wikipedia.org/wiki/Matrix_multiplication (or any linear algebra textbook): For matrix multiplication, the ...
• 2,646

### Calculating the force and/or torque required to pivot an arm from one end

My calculation got the same answer as you. Here's what I did. You mentioned that the arm has some weight so I added that force to your diagram. Also, I labeled the center of the elbow joint as ...
• 61
Accepted

### What is the first moment area of a rounded rectangle?

I don't have a simple formula but that is the way i would handle it. Assuming the four corners are circular with equal radius r, so that symmetry exists, the first moment of area of one half of the ...

### Is radians a dimensionless quantity?

TL/DR As the other answers have stated, radians are dimensionless. Cycles and Turns This is a question that seems to come up often, and from many different quarters; not only from students and lay ...
• 1,166

### What program to implement mathematical models?

"Numerical Recipes" is probably what you need the most. It contains tons of useful scientific/numerical computation codes. It's a book, but I believe it was also available online. Apart from that, ...
• 906

• 623

### How do enginners build highway interchanges ? Are highway interchanges build based on a mathematical theory such as braids and knots theory?

It's much closer to graph theory. First, traffic projections: basing on known and projected urban data - habitation, production, recreation, trade zones, transit, etc, the general transition patterns ...
• 6,105

### linearizing a non linear state space equation

The Lagrangian for your 1D pitch system is $\mathcal{L} := T - U$, which is $$\mathcal{L} = \frac{1}{2}(mb^2 + Ma^2)\dot{\phi}^2 + \frac{1}{2}J\dot{\theta}^2 + (Ma - mb)g\sin\phi$$ The Euler-...
You can switch to the frequency domain to look at the transfer function of the system. For you particular case, taking the Laplace transform of both sides gives  sY(s) = -kY(s) + U(s) + \frac{a\...