1. ### Calculate a specific boost and rotation

Let's begin with the first point. a.I) Apply a generic boost in the y-z plane (take advantage of the arbitrariness in deciding the alignment of the y and z axes). \begin{equation*} B_{yz} = \begin{pmatrix} \gamma & 0 & -\gamma v_y & -\gamma v_z \\ 0 & 1 & 0 & 0 \\ -\gamma v_y & 0 &...
2. ### B Energy to increase the radius of a circle composed of several disks

Hi, I take a big number of disks to composed a circle of a radius of 1 m, the blue curved line is in fact several very small disks: I take a big number of disks to simplify the calculations, and I take the size of the disks very small in comparison of the radius of the circle. The center A1...
3. ### Forces at the bottom of a rotating U-tube filled with water

So when the rotation starts some water will move upwards and in the vertical part of tube. I know hat centripetal force will be given by F=mv²/r Now I though of taking r as centre of mass of the water system but I don't know what to take the value of m as? Should I only consider the water...
4. ### Disk rotating in a disc

From a freebody analysis I got, $$\vec{r} \times \vec{F} = |r| |F| \sin( 90 - \theta) = (R-r) mg \cos \theta$$ and, this is equal to $$I \alpha_1$$ where the alpha_1 is the angular acceleration of center of mass of small circle around big one, $$I \alpha = (R-r) mg \cos \theta$$ Now...
5. ### I Confusion About Rotational Motion

I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
6. ### Minimum force required to rotate a lamina

When the lamina rotates about A, FA must act on B (because it is the farthest away) perpendicular to AB (so that all of FA contributes to rotation). Same argument is valid for rotation of lamina about B as well. Having noted that, I tried two approaches: Approach 1- If I assume that the...
7. ### I Rotation of functions

I was solving a problem for my quantum mechanics homework, and was therefore browsing in the internet for further information. Then I stumbled upon this here: R is the rotation operator, δφ an infinitesimal angle and Ψ is the wave function. I know that it is able to rotate a curve, vector...

29. ### How to calculate angular speed?

Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...
30. ### I Rotating sphere which separates into hemispheres

Hi all, The scenario I'm considering is a solid sphere (of uniform density) rotating with constant angular velocity when it abruptly splits into two hemispheres along a cut which contains the rotation axis. The hemispheres will begin to separate; if, for example, we consider the rotation to be...