17 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.
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  • 979
12 votes
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How can I determine a function equation from a graph image?

I don't know how this function was obtained (or what it is supposed to represent). But you could try searching the literature to see if someone has published equations of the curves. However, looking ...
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9 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 ...
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  • 1,876
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. ...
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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, ...
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  • 2,511
7 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{\...
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  • 2,149
6 votes

What are the meanings of the second argument to the convolution?

I think the diverse range of names for the second argument arises from the fact that the convolution operation is so useful in so many different fields. It is helpful to recall what the convolution ...
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6 votes

Differential equations of a (simplified) loading bridge

Kinematics and dynamics Those are the steps to solve problems of this nature. Analize the kinematics of the system. $\hspace{5.em}$ $_{o}\vec{r}_{OP}$ = $_{o}\vec{r}_{OR}$ + $_{o}\vec{r}_{RP}$ $\...
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6 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 ...
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5 votes

Derivation of the weak form for the euler-bernoulli beam equations

It's easier to understand this identity if you start with the partial differential equation for the Euler-bernoulli beam deflection equation $$\frac{d^2}{dx^2}\left[ EI \frac{d^2u}{dx^2}\right] = 0$$ ...
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  • 2,559
5 votes
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Differential equations of a (simplified) loading bridge

My guess is that you probably need another differential equation for the angular movement, that will involve the inertia, such as: $$m_G l^2 \ddot{\varphi} = m_G g l \sin(\varphi)$$ which yields: $$...
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  • 1,806
5 votes

How do I properly compute mean time to failure?

First off, always remember that garbage in = garbage out; so if your data is garbage then your statistics will be garbage. In this situation your optimal data would be something like Run Hours Until ...
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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 ...
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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", ...
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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 $...
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  • 1,603
5 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 ...
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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, ...
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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 ...
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4 votes

How can I determine a function equation from a graph image?

You have a single-valued function dependent of two variables. There are many ways to model that. If you know something about what this function represents, then going back to the physics might yield ...
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4 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 ...
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4 votes

How do I properly compute mean time to failure?

If you don't have hard data, making assumptions (preferably "reasonable" ones) is the only option you have. (Maybe that's why engineers used to call their slide rules "guessing sticks...") You can't ...
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  • 12.5k
4 votes
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Steady state value, a possible shortcut?

Think for a moment about what it means for $\eta(t)$ to have reached its steady state. It means precisely that $\dot{\eta}(t)=0$. If you plug that into your first equation and solve for $\eta(t)$ ...
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4 votes
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Uncertainty Calculation of LVDT displacement transducers for length measurement

For the Maths of calculating uncertainty the standard document is the GUM. Which describes all the maths but can be somewhat unclear if you don't already have some idea how it is supposed to work. ...
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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. ...
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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 ...
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  • 3,525
4 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 ...
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4 votes
Accepted

Difference between partial derivatives and derivatives in physics

For a detailed explanation search WikiPedia for derivative, partial derivative and ...
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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 ...
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  • 21k
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 +...
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3 votes

Modifying a fixed camera lens for close focus

I think you are misinterpreting what your variables are. The focal length is fixed for a given lens and cannot be changed. What you can change is the image to lens distance. Combined these will ...
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