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comment Why we use liquid crystals in LCDs?
It does not. Have you seen the video?
comment Conservation of mechanical energy isn't giving me the right answer?
Mechanical energy is not conserved when there is a friction so you cannot use this method. You can verify it in simpler case: Suppose you pushed the package on a flat surface - its potential energy does not change, yet the package will lose kinetic energy as it will stop due to friction. Mechanical energy is not conserved - some/all of it will escape the system as heat.
comment Why is the gravity in a mine shaft independent of depth if the local density is 2/3 of the average density?
Can you cite a source? Assuming homogenous earth, gravitational acceleration decreases linearly with depth, with zero at the center of earth. I don't know what you call a "local density", but any density disturbances close to the shaft should not have a significant effect.
comment Error propagation with dependent variables
How do you compute $y_F$ ? Do you measure it by measuring $f(y)$ also for other values of $y$ and then compute the integral, or some other method gives you $y_F$ directly? Do you know the shape of $f()$?
comment Maximum reading after dropping a mass onto a scale
I think you are right that approximating scale just as a spring is unrealistic. This is because in fact it is heavily damped! When you step on the scale, it takes it only a few oscillations to stabilize. That means the first spike might be significantly lower compared to the undamped case. This however introduces new unknown quantity - damping constant, but I guess we would be able to estimate it if we measure the time it takes the scale to stabilize. By measuring frequency of the oscillations we can also improve our estimate of spring constant.
comment Accelerating a glass of a water across a table?
This is almost true, just that in the reference frame of the glass, the acceleration of the glass presents itself as inertial force in the opposite direction (the g is also equivalent to glass accelerating upwards, not downwards). So the picture is incorrect. Water level will be higher on the back side of the glass.
comment Rigid body dynamics joints
Sorry, I should've included the article name. It's "Advanced character physics" by Thomas Jakobsen. It's pretty well googlable.
comment Conservation of Energy and the Poynting Theorem
As I can't comment on the question above, I have to do it here: Dear ganzewoort, perhaps you should have commented here, rather than modyfying your question, thus disrupting the chronology of posts. As of the subject matter, you could have clearly read in my reply that I basically agree with you. Poyinting vector is rendundant in your sense. However, in the same sense the energy conservation law is also redundant, as it is fully derived from Maxwell equations, therefore states nothing new.