# Tag Info

## New answers tagged geometry

7

Here's a slightly more accurate diagram: It's still not quite to scale — the Moon is actually a lot further away from the Earth than shown here — but it should suffice to demonstrate that the moon can indeed be seen from the night side of the Earth even when it's nearly between the Earth and the Sun. Note how, in the orientation shown in the ...

8

Your diagram is not quite to scale, and the errors are important. Notice that only the hemisphere of the moon which points toward the sun is illuminated, rather than what your drawing shows. This has the following implications. 1) When the moon is new, it rises and sets at the same time as the sun, and is not (mostly) visible at night. The extreme example ...

1

Your derivation is correct, although your assumption about $v$ (it's constant) must be made before evaluating the relevant integral. Physically speaking, make the transformation to the moving frame: $y' = y$ $x' = x - vt$, and the implicit form becomes $y'^2 + x'^2 = R^2$. So, this is indeed a cycloid, because we see a circular path in the moving frame. ...

-2

It might not be as mysterious as it appears. Pi is only the consequence of converting from one coordinate system (orthogonal) to another (spherical). This exceeds my cleverness, but I think if one created another coordinate system (with some axes 30 degrees apart instead of 90) then there would be some square roots (which are also irrational) in the ...

1

Strange question. This should probably be on MathSE. There are a million proofs of the irrationality of pi, and why it has to be irrational. You need some reasonable Mathematical knowledge to understand them - it's not like proving the irrationality of root 2. I encourage you to have a look!! As for the whole "it just is" thing... "It just is" isn't the ...

0

There is a easy semi-geometrical way of finding the center of rotation due to a force. Find the moment arm $c$ of the force through A. $$c = r \cos \theta$$ Find the radius of gyration about the center of mass C $$\rho = \sqrt{ \frac{I_C}{m} }$$ Measure the distance $\ell$ away from the center of mass and mark point R $$\ell = \frac{\rho^2}{c}$$ Point ...

0

I think what you are asking about is answered by the fundamental theorem in the mechanics of rigid bodies, which states that the motion of any rigid body can be decomposed into the motion of its center of mass (not necessarily rectilinear) and a rotation about its center of mass (COM). The two statements you emphasize are direct corollaries. Please see ...

0

I am correctly understanding that this is for the mass moment of inertia and not something else like the area moment of inertia right? No. The formula given are for the area moment of inertia. Although you can essentially use them to find the moment of inertia just by multiplying the answer, you get using this formula by the area mass density of the ...

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