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 &...
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...
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...
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...
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...
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...
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...
Below is the attempted solution of a tutor. However, I do question his solution method. Therefore, I would sincerely appreciate it if anyone could tell me what is going on with the below solution.
First off, the rotation of the matrix could be expressed as below:
$$G = \begin{pmatrix} AB & -||A...
It's often said that you don't feel earth rotation because the gravity acts against the centrifugal force.
Of course this is true but also your body is turned around once each 24 hours.
So I wonder on a planet which is rotating once each 3 seconds and has same g=9,81:
Would you feel the rotation?
I was talking to someone about the equilibrium of fluids and we reached at some stage where we had to prove that in an external field the translational forces add to zero along with moments (torques) should also add to zero. The first one was quite easy but during the discussion of second...
Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects.
The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment...
Summary:: Calculating the inclination angle
A stick is on two springs with spring constants D1=500N/m and D2=300N/m. Consider the stick is without mass and can rotate around the point E, which is distant from spring 1 with 0,1m and from spring 2 with 0,8m. A force F=100N pulls the stick up...
I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again:
##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[
\begin{pmatrix}...
For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
Answer choices: N2L for Translation, N2L for Rotation, Both, Either
1. You are asked to find the angular acceleration of a low-friction pulley with a given force exerted on it.
My solution = N2L for rotation
2. You are asked to find the angular acceleration of a low-friction pulley due to...
A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...
(The answer given in the text says ##\boxed{T_1\; >\; T_2}## but, as I show below, I think it's just the opposite).
I begin by putting an image relevant to the problem above. Taking a small particle each of the same mass ##m## at the two positions, the centripetal forces are ##T_1 =...
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
First off, I was wondering if the acceleration of the conveyor belt can be considered a force. And I'm not exactly sure how to use Newton's second law if the object of the forces is itself on an accelerating surface.
Also, I don't know whether it rolls with or without slipping.
I thought I could...
Hi Everyone!
I am trying to a DIY project to make a food maker. I am 50% succeeded with that and need help for the remaining 50%.
The idea is to produce the output shown in the first image. That food is made with a flour. So I have the setup a pressing machine shown in image2. In this I was...
Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure.
Find the maximum velocity the ring must roll so that it doesn't...
It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.
Problem Statement: i have a steering wheel mounted on an electric motor, and i want to stop the driver from going beyond a certain angle. i can read the torque applied by the driver, and the steering wheel angular velocity as well. how can i stop the steering wheel, without sending it harshely...
For parts A and B I used energy to find the vcom and omega, but that won’t work for C. I have an answer by combining the three formulas that use acceleration above. My answer for alpha=-5g/3r. The next two are easily solvable if you find C, but I still feel like I’m missing something. Any help...
Hello everybody,
I am currently working on an experiment investigating the formation of planets.
I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together).
From the imagery I can see those agglomerates which are build up by smaller...
This question is from 1977 AP Physics C so I suppose it would be clear enough, but I am confused about question c. Question a is easy (it rotates counterclockwise), question b too (Στ=6*rxF=6*r x (I*i x B)=0.06). Question C is where I am stuck.
The diagram provided with the question looks like...
$$mg(0.45) = mg(R + R \cdot cos(\frac{π}{3})) + \frac{1}{2}mv^2$$
$$v^2 = g(0.9 - 3R)$$
The centripetal acceleration during the "flying through air" will be given by gravity
$$mg \cdot cos(\frac{\pi}{3}) = \frac{mv^2}{r}$$
$$R = \frac{1.8}{5}$$
But my book says $$ R = \frac{1}{5}$$
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...
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...