Recent content by TysonM8

To answer this question properly, forget about the magnetic force for a moment. If the velocity of a charge outside the wire is stationary relative to the positive metal ions, the positive and negative charge densities in the wire are equal. If however, the charge is moving at some velocity v...

The Work-Energy Theorem only applies to rigid bodies. That is, if the work is not used to deform the object. There's a thread here that discusses this in detail; http://physics.stackexchange.com/questions/58134/how-to-understand-the-work-energy-theorem Work by definition, is what a...

I found this proof satisfactory; https://www.khanacademy.org/math/calculus/differential-calculus/der_common_functions/v/proof--d-dx-e-x----e-x

This appears to be an application of the reverse product rule. Starting from the second step and working backwards; -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ} (\frac{∂L}{∂(∂_{μ}\phi)} δ(\phi)) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) +...

OMG I knew these course descriptions sounded familiar. Interesting that I found another Australian on an American forum. I was going to go to ANU to study theoretical physics (got accepted to the Bachelor of Advanced Science), but ended up choosing The University of Melbourne. It's a shame I...

I know how to solve linear systems but I came across this question where I've never seen the notation before. I searched all over the internet but still couldn't figure it out. The question asked to find all solutions in Z_{2}^{5} of a linear system. I'm guessing that Z^5 means all integers on...

That's the first time you reverse the bounds (you also do this for the second step, reversing the bounds a and b), but you reverse the bounds of the second integral (g_1(x) and g_2(x)) later on. The question is, why isn't this done for the second step as well?

I’m having a little trouble understanding why Green’s Theorem is defined as; ∮_C P dx+Q dy = ∬_D [(δQ/δx)-(δP/δy)] dA Instead of; ∮_C P dx+Q dy = ∬_D [(δQ/δx)+(δP/δy)] dA When proving the theorem, in the first step you simply reverse the bounds of the second integral to get the...

The problem is the two formulas you have created (a=g/sinx and a=gsinx), use different angles. The first formula you created uses the angle between the ramp and the earth. The second one uses the angle between the vertical axis and the direction of acceleration. So both formulas are correct but...

Thanks for all the advice guys :) I've still got a long way to go anyway, so I shouldn't be too concerned at the moment. Even if I won't end up doing research in the long term, I'm still going to study physics for the fun of it.

I'm in year 12 and I will be studying math and physics next year. I love physics and I'm hoping to do a PhD in the future. Let's say I make it that far, the job prospects are terrible. If I end up having to get a job in finance or something, will I be able to do research in my spare time? You...

Ok, I'm really confused with the reasoning behind inductive proofs. To prove some statement is true for all natural numbers, you need to assume the statement is true for some number k. But aren't you really assuming the statement is true for all natural numbers in the first place? If you can...

EDIT: Figured out question, don't worry guys.

c∫d α∫β 1∫2 ρ^2 sin∅ dρd∅dθ = c∫d α∫β [(ρ^3)/3 sin∅] [1,2] d∅dθ = c∫d α∫β 7/3 sin∅ d∅dθ = c∫d [-7/3 cos∅] [α,β] dθ = c∫d [-7/3 cosβ] - [-7/3 cosα] dθ = c∫d 7/3 (cosα - cosβ) dθ = [(7θ)/3 (cosα - cosβ)] [c,d] = [(7d)/3 (cosα - cosβ)] - [(7c)/3 (cosα - cosβ)] = (1/3)(7d-7c)(cosα - cosβ) This is...

The ladder paradox can be resolved when considering the relativity of simultaneity. However, wouldn't the problem be unsolvable when thinking of it in terms of general relativity? For instance, if the ladder was stationary relative to the earth, and the barn was accelerating towards the ladder...