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14 votes
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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.
agentp's user avatar
  • 949
10 votes

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 ...
Suba Thomas's user avatar
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7 votes

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. ...
Olin Lathrop's user avatar
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7 votes
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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, ...
Daniel K's user avatar
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6 votes
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How to Derive the Differential Form of the Contintuity Equation

for $y = f(x_1, ..., x_n)$, the sum of the partial differentials with respect to all of the independent variables is the total differential: $$ dy = \frac{\partial y}{\partial x_1}dx_1+...+\frac{\...
Algo's user avatar
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5 votes
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Square wave transfer function?

I thought I would expand a little on the answer offered by Karlo. Long story short, I would not try to calculate the analytical time response of a system to a square wave. That would be a serious ...
ConjuringFrictionForces's user avatar
5 votes
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Determine the moment of inertia of a filled circular sector

Since you actually asked for the moment about the $x$ axis. Calculating the moment of inertia about the $x$ axis is a fair deal more complicated than calculating it about the $z$ axis as in my other ...
Chris Mueller's user avatar
5 votes
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Difference between partial derivatives and derivatives in physics

For a detailed explanation search WikiPedia for derivative, partial derivative and ...
user883521's user avatar
5 votes

Is engineering basically controlling oscillators?

No. First, there is much much more to most engineering disciplines than analyzing the response of something. Second, even when that is part of the task, it isn't done by "adding oscillators", ...
Olin Lathrop's user avatar
  • 11.4k
5 votes

Frequency Response of a Discrete System

If you want to evaluate a continues time transfer function at a specific frequency $\omega$ in rad/s you substitute $s$ with $j\,\omega$. For a discrete time transfer function you substitute $z$ with $...
fibonatic's user avatar
  • 1,653
5 votes

Should Engineers Understand Equations without Relying on Derivations?

Knowing the derivation is important because it usually tells you what initial assumptions were made in the derivation and what the limits of applicability of the resulting equation are. Understanding ...
niels nielsen's user avatar
5 votes

Can you offer real-world examples of logarithm use?

Following are a few examples of logarithmic use. Some well know (like Richter and Decibel), some other more morbid (like pH, or spreading of diseases). On each example, you could write a full answer, ...
NMech's user avatar
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4 votes

Applications of the Laplace Transform

I think you are neglecting the broad range of applications included in solving 'some kind of differential equation.' At the very basic level of physics, everything we know about the world is ...
Chris Mueller's user avatar
4 votes
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3D Transformation Between Two Cartesian Coordinate Systems Using Euler Angles

Suppose Frame 1 is a world coordinate frame and Frame 2 local robot frame. The thing that's a little confusing here is that when you transform from Frame 1 to Frame 2, you are saying that you want ...
Chuck's user avatar
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4 votes
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Help an electrical engineering student with a beam deflection question

Yes. The first derivative of the deflection is equal to the tangent of the deflection, which for small deflections can be approximated as equal to the angle of rotation of the beam at each point. ...
Wasabi's user avatar
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4 votes
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Should Engineers Understand Equations without Relying on Derivations?

Should I, as an engineer-in-training hoping to complete research, focus on trying to understand equations to my satisfaction, or should I instead just become well acquainted the equations, their use ...
Jeffrey J Weimer's user avatar
4 votes

How can I implement S-curve motion profile on mobile robotic platform / wheeled robot?

There are many ways to create a trajectory between two points using a sigmoid function. It's not a simple question, and the math is a little involved. Here's how I would do it. Short Answer You can ...
BarbalatsDilemma's user avatar
4 votes

Swing safety: maximum load of beam (supported at one end, free with load on the other)

I would recommend you have your boys wear a helmet while playing. Also cover the landing area with 8 inch deep bed of mulch or some soft material like foam sheets covered by a mat. With all due ...
kamran's user avatar
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4 votes
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Stretch in Infinitesimal strain theory

Taylor is straightforward: $$ \sqrt{1+2x} =\left.\sqrt{1+2x}\right|_0 +\left.{d \over dx}\sqrt{1+2x}\right|_0x +O(x^2) \\ =1 +\left.{d \over dx}{1 \over \sqrt{1+2x}}\right|_0x +O(x^2) \\ =1 +x +...
Brethlosze's user avatar
4 votes

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 ...
Daniel K's user avatar
  • 2,646
3 votes

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 ...
abqsteve's user avatar
3 votes
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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 ...
minas lemonis's user avatar
3 votes

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 ...
Rick's user avatar
  • 1,166
3 votes

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, ...
Gürkan Çetin's user avatar
3 votes

Convert angular acceleration from (S/100Hz) to (RPM/s)

$\frac{s}{100Hz}$ has basic unit dimensions of $[time]^2$, and as such is not a unit of angular acceleration. You cannot convert directly between these two quantities. First, we can convert from $rpm/...
Jonathan R Swift's user avatar
3 votes
Accepted

Is there any defined mathematical parameter that can give me the average distance of a volume to a point?

First, let's consider a Cartesian plane with the loading platform at the origin. It is obvious that the distance to any point is on the plane is: $l = \sqrt{x^2+y^2}$. If you extend this to the $3^{...
ChP's user avatar
  • 623
3 votes

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 ...
SF.'s user avatar
  • 6,105
3 votes

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-...
Josh Pilipovsky's user avatar
3 votes

Input-output representation to state space

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\...
Josh Pilipovsky's user avatar
3 votes
Accepted

Help understanding a control system represented by coefficients of theta?

In mathematics,which are very closely related and broadly applied in control engineering, the derivatives with respect to time are often notated using the so-called: dot notation. You can check this ...
Teo Protoulis's user avatar

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