# Tag Info

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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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### 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 ...

### 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 ...

### 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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### 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, ...

### 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 ...

### 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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### 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. ...

### 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 ...

### 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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### 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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### 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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### 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 ...

### 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 ...

### 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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### 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 +...

### 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 ...
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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 ...
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### Equating $\frac{dp}{dt}$ and $F$ at a hydraulic jump?

$F=\frac{dp}{dt}$ is, in some sense, a more fundamental expression of Newton's law than $F=ma$ because $F=ma$ doesn't allow for situations with changing mass. You can easily derive the second from ...