Recent content by powerof

Can you expand on this or give me some resources to study on my own? Thank you.

While investigating about the curl I have found this interesting perspective: http://mathoverflow.net/a/21908/69479 I lack the knowledge to do the derivation on my own so I would like to ask for your help. I am an undergraduate. I do not understand what a "first order differential operator"...

When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##? \frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...

Thank your for your help. The counterexamples definitely make this inequality impossible, so a typo it must be. Have a nice day!

Homework Statement [/B] Prove the following: \sum_{k=1}^{\infty}a_{k}^{2} \leq \left ( \sum_{k=1}^{\infty}a_{k}^{2/3} \right )^{1/2} \left ( \sum_{k=1}^{\infty}a_{k}^{4/3} \right )^{1/2} Homework Equations [/B] The following generalization of Cauchy-Schwarz present in the text (containing...

Ooops, that was a blunder. \vec{a_{cm}}=l\ddot{\theta}(-\sin\theta\vec{i}+\cos\theta\vec{j})-l\dot{\theta}^{2}(\cos\theta\vec{i}+\sin\theta\vec{j}) I have calculated it again taking into account what you said. The above is indeed correct. We can check by observing that the second parenthesis...

I come back to your question. Thinking it over again, I see that indeed it must have a centripetal component, if not the velocity with respect to the center of mass would not change direction. So ##\vec{a^*}=\vec{a_c}+\vec{a_t}##, where the modulus of a_t is L/2*alpha. \vec{a_p} = \vec{a} +...

Using geometry as you said I get that the distance of the center of mass to the point O, which I take to be the corner formed between the wall and the ground, is constant, independent of the angle and even more, that distance is half the length of the rod, that is, L/2. The center of mass then...

Oh, I was wrong at least there then. I assumed that a^*=0.5L alpha (that's just the perpendicular component). Energy perhaps? It's 1 am here so I'll get on it tomorrow.

I don't know where to start when analyzing the general motion of the rod. For the moment I'll just try to set N_wall=0 and see what comes out. \tau_{total} = I^* \alpha = N_{ground}\frac{L}{2}cos\theta - N_{wall}\frac{L}{2}sin\theta = \frac{1}{12}ML^2\alpha (Ma+Mg)\frac{L}{2}cos\theta =...

I think I see it now. It might just mean that the center of mass is decelerating if it was previously moving to the right. But if this is the case then it doesn't make sense to describe the normal with that equation, at least not in said case (decelerating horizontally). Does this mean my...

Oh, yes, now I understand what you meant. You can sum and rest Xcm to Xa and get the following equation, where x* is the position with respect to the cm. \vec{x_a}=\vec{x_a}+\vec{x_{cm}}-\vec{x_{cm}}=\vec{x_{cm}}+(\vec{x_{a}}-\vec{x_{cm}})=\vec{x_a}+\vec{x^*_a} We can do the same thing with Xb...

I'm not sure what you mean. The vector v1 from the CM to the first endpoint, the one tangent to the wall, has a length L/2. The vector v2 from the CM to the point tangent to the ground is also L/2. If it were not a rod but a system with two particles each with some masses m1 and m2 but at the...

Homework Statement [/B] As a diagram any of the countless images on the internet serve well: Suppose the static friction was not sufficient to maintain the rod in a static equilibrium and it starts slipping/sliding. It has an initial angle theta with respect to the ground. Assume there is no...

That is most definitely easier than what I was doing. For some reason writing the solutions as v_{y}=C_{1}\cdot\sin(C_{2}t+C_{3}) and v_{x}=\frac{g}{K}+C_{1}\cdot\cos(C_{2}t+C_{3}) makes determining the constants harder. In any case, thank you for your help. Knowing what the constants are will...