Recent content by raving_lunatic

Homework Statement So this is part of a broader problem about the quantum harmonic oscillator, but there's one particular bit of mathematics I'm stuck on. We have the differential equation: y''(x) +(ε-x2) y = 0 And I'm told that we're to examine how y behaves as x tends towards...

I'm guessing the axis of rotation is the one that passes through the center of mass, parallel to the surface? (There's only two that seem to make sense to me.) Okay - so we have a combination of translational motion of the CM and rotational motion about the CM in the case where the edge of the...

Homework Statement A cube of mass m and side 2a is held on one of its edges on a horizontal surface. It is released from this position and allowed to tip. Find an expression for the angular velocity of the cube as its face strikes the surface of the table in the following cases: a) the...

Sorry LC Kurtz and others - maybe I didn't make it clear - expressing x and y in terms of u and v was a part of the problem that we were explicitly asked to do - which seemed strange because it wasn't necessary, under normal circumstances I'd tackle the integral straight away The quadratic in...

Are the axes you're rotating about x = -1 and y = 5? As in, these are two separate parts of one question? I suggest a change of variables here. You can redefine the axes (shifting everything to the left, right, up or down) and then use the formulae you know to find the surface area of...

Homework Statement This problem seems fine but has me stumped for some reason... For the variables u=x2−y2 v= x y Under the condition u>0 We're simply asked to determine x(u,v) and y(u,v) so that we can eventually use them to solve a multiple integral by substitution. Homework Equations...

Homework Statement Hi, everyone. Me again. This time I'm here to ask about the tension in the string on a massive pulley. We have a wheel of radius R with a moment of inertia about its principal axis of 2/3 MR2 , suspended above the ground on frictionless bearings. A massless string of...

Homework Statement "Consider a cable, of fixed mass per unit length, which extends radially from just above the surface to a distance ηR measured radially from the center of the Earth. By determining the total force on the cable, or otherwise, find an expression and numerical value for η. At...

Homework Statement Hi! This is probably going to be a silly question, but I think I just need someone to point out my obvious mistake so I can go back and solve it properly. A semi-infinite string of density ρ and tension T has a mass affixed to the free end which is constrained to move...

Thank you so much! I think I get it now. I had a vague idea that it was to do with the symmetry between r and r' in this expression but for some reason didn't think to use chain rule. As usual, reducing the problem to a single component helps. Thank you.

Thank you for your reply. I'm still a little confused, but your answer has given me something to go on. Let me see how this sounds: We're considering the function ψ = ∫f(|r-r'|)d3r' which is a scalar function in terms of r (after the integration is performed.) As the function is...

Homework Statement Hi, it's me again. I'm new to vector calculus so this might sound like a stupid question, but in relation to a specific problem, I was wondering when we could move the del operator under the integration sign - in relation to a specific problem, which is: A(r) = integral...

Homework Statement Hi! Bear in mind, before shooting me down, that I'm very new to electrostatics and extremely (i.e. today) new to the method of image charges, and all my learning is dodgy book-learning and not learning from asking the learned questions. This said, I just want my...

I think I've worked it out; need to keep the terms to the second order. Sorry.

lbix asked a perfectly reasonable question. Do you know an expression for the magnitude of the dot product of two vectors? Do you know, for example, what the dot product between two vectors signifies geometrically?