Search found 474 matches

by joe
Mon Sep 14, 2015 9:57 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

In the first one, d A = dx dy so A = integral dx dy = delta x * delta y For the other one, the question is not very clear. But if the field is F k , where F is constant and k is the unit vector in the z direction, then, from the definition of flux, the flux is just integral F k . d A 2 = integral F ...
by joe
Sun Sep 06, 2015 7:19 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

In the sketch shown, F is obviously not the total force. (BTW not all the F vectors are at right angles to the curve) A case where the total force on an object is at right angles to its trajectory is uniform circular motion (not the case here) If this sketch comes from a course offered by someone el...
by joe
Thu Sep 03, 2015 11:45 am
Forum: Physics Questions
Topic: Mathematical obscuration?
Replies: 30
Views: 27755

Re: Mathematical obscuration?

I don't understand the problem here. Even if the coefficient of a differential is very large, one can still make the product very small by taking a very, very small differential.
by joe
Thu Sep 03, 2015 11:44 am
Forum: Physics Questions
Topic: Differential equations?
Replies: 2
Views: 6158

Re: Differential equations?

The vector grad(V) is perpendicular to equipotential surfaces V = constant.
For me, 'line integral curve' means the curve along which one calculates a line integral. Its shape is arbitrary - you can choose it to be whatever you like.
So I don't see a problem.
by joe
Thu Sep 03, 2015 11:02 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

So far as I can see, if grad(V) exists, it is always at right angles to a surface of equal V.
Perhaps the surfaces are not equipotentials. Or perhaps the author means something different when s/he says gradient vector. For instance, be aware of the difference between gradient and gradient vector.
by joe
Thu Sep 03, 2015 8:42 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

The first link you give is not explained. However, I guess that the surface it shows is an equipotential (e.g. a surface of constant voltage V(x,y,z) ) and the normal vector it shows is the gradient vector (e.g. grad(V), which is minus one times the electric field). I didn't watch the video (busy). ...
by joe
Sat Aug 01, 2015 12:50 pm
Forum: Physics Questions
Topic: Inertia in Linear and Rotational motion?
Replies: 21
Views: 35189

Re: Inertia in Linear and Rotational motion?

For the rotation about an inclined axis, you'll need to specify components in all three dimensions. Also, you need to be careful about two things: - if the mass is on a spring, rather than an inextensible string, then its path will not be circular: the spring will be longer at the bottom. - in the a...
by joe
Thu Jul 30, 2015 10:01 am
Forum: Physics Questions
Topic: Inertia in Linear and Rotational motion?
Replies: 21
Views: 35189

Re: Inertia in Linear and Rotational motion?

Your second question:
What makes the object go at the tangent direction (tangent velocity direction) after being released?
Newton's first law of motion.
by joe
Thu Jul 30, 2015 10:00 am
Forum: Physics Questions
Topic: Inertia in Linear and Rotational motion?
Replies: 21
Views: 35189

Re: Inertia in Linear and Rotational motion?

The angular momentum L = r X p = r X m v where the vector cross product is defined here http://www.animations.physics.unsw.edu.au/jw/vectors.htm#cross if you need it. Note that L depends on which origin one uses, though of course for circular motion one usually chooses the center of the circle. Note...
by joe
Wed Jul 15, 2015 11:26 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

I don't mind calculus being discussed here. Within limits, I don't mind helping out MIT. But, because it is a wealthy, well-resourced institution, I'd rather not make a habit of it.
by joe
Wed Jul 15, 2015 8:57 am
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

Gday Boris I think that you might be confusing some related but different issues here. z = a_1*x + a_2*y is a plane in 3 dimensions. The slope of this plane in the x direction is a_1. To make an analogy with w = a_1*x + a_2*y + a_3*z you need 4 dimensions, which is impossible to visualise, and hard ...
by joe
Sat Jul 11, 2015 4:42 pm
Forum: Physics Questions
Topic: Multi-variable systems?
Replies: 43
Views: 37541

Re: Multi-variable systems?

What kind of stuff may be related to multi-variable function f(x,y,z) (with 3 variables)? A good example is electric potential, V(x,y,z). You can then get the field components by taking partial derivatives E_x = - ∂V/∂x etc. Similarly, for the concentration C(x,y,z), the components of diffusion are...
by joe
Thu Jun 18, 2015 10:24 pm
Forum: Physics Questions
Topic: What is beyond Newton's and Einstein's discoveries?
Replies: 34
Views: 25983

Re: What is beyond Newton's and Einsteins's discoveries?

Gday Boris In 2005, the centenary of relativity, the School webmaster and I put a lot of effort into making an introduction to relativity that could be readily understood. Go to Physclips http://www.animations.physics.unsw.edu.au and, at bottom right in the main screen, see the link to relativity. S...
by joe
Wed Jun 17, 2015 8:52 am
Forum: Physics Questions
Topic: The Em Drive - Does it violate conservation of momentum?
Replies: 1
Views: 5389

Re: The Em Drive - Does it violate conservation of momentum?

It's always difficult to assess something that has not been formally published. Newspapers and popular magazines like New Scientist (relevant here) do not insist on the same levels of detail and rigour that are expected in scientific journals. As a result, there's a lot of skepticism about this stor...
by joe
Wed Jun 03, 2015 9:43 pm
Forum: Physics Questions
Topic: What is beyond Newton's and Einstein's discoveries?
Replies: 34
Views: 25983

Re: What is beyond Newton's and Einsteins's discoveries?

Interesting example to choose: there is a famous essay about consciousness by the philosopher Nagel called 'What is it like to be a bat' http://en.wikipedia.org/wiki/What_Is_it_Like_to_Be_a_Bat%3F I would argue that we understand radio waves fairly well, even though we can't perceive them directly (...