Recent content by Teclis

Yes, so you think the answer in the Textbook has just been unintentionally truncated?

Thanks, you are correct it is a typo. I do in fact have ##\sin{\phi}## in my paper calculations and not ##\cos{\phi}##

I am trying to solve the following problem from my textbook: Formulate the vector field $$ \mathbf{\overrightarrow{a}} = x_{3}\mathbf{\hat{e_{1}}} + 2x_{1}\mathbf{\hat{e_{2}}} + x_{2}\mathbf{\hat{e_{3}}} $$ in spherical coordinates.My solution is the following: For the unit vectors I use the...

Thanks, I found a good explanation of the notation in Mathematical methods in elementary thermodynamics S. M. Blinder Chem. Educ. 1966, 85-92 https://doi.org/10.1021/ed043p85

On Page 406 of Nolting Theoretical Physics 1 he has the following notation for the Jacobian determinant $$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} = \begin{vmatrix} \left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}}...

Using A = x0, B = v0/ω I get ω = 4π, A = 1, B = 1/4π then converting to phase/magnitude form \sqrt{A^{2} + B^{^{2}}} = \alpha \sqrt{1^{2} + \left ( \frac{1}{4\pi }\right )^{^{2}}} = \alpha = \frac{1}{4\pi }\sqrt{16\pi^{2} +1} However the answer in the back of the book has α = 1 Is...

Yes I understand this.

Yes I understand vector algebra I arrived at this topic from working on question 41 of chapter 13.5 of Marsden and Weinstein Calculus III. I understand linear motion so I would answer that acceleration is the ratio of Force to Mass.

Hi, Thank you very one for taking the time to answer my questions and explain things to me. I think I found the answer I am looking for in video number 14 from the following web site: http://www.gyroscopes.org/1974lecture.asp The presenter states that moment inertia and angular momentum are...

Wouldn't the centripetal acceleration also be a torque?

Yes but the torque vectors in the gyroscope are not in the same location. The torque vector from gravity is in the center of the gyroscope as is the angular momentum vector, but the torque vector from the circular motion produced by the angular momentum would have to be on the circumference of...

I thought torque was equal to the moment of inertia multiplied by the angular acceleration? And angular momentum is moment of inertia multiplied by angular velocity? In gyroscopic progression the fixed points from which the radii are measured is different so it doesn't make sense why we should...

In studying gyroscopic progression, the angular momentum vector is added to the torque vector. As intuitively these two vectors seem to be qualitatively quite different, how do we know that both vectors are in the same vector field and that they can be manipulated using the rules of vector...

pg. 243 Falconer, I. (1987) Corpuscles, Electrons and Cathode Rays: J.J. Thomson and the Discovery of the Electron. The British Journal for the History of Science (BJHS, 1987,20,241-276). "One of their most important properties is that they are deflected by a magnetic field. This provided strong...

On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...