Rotating Definition and 1000 Threads

The world building thread about a derelict spaceship got me wondering. An object can rotate on two axes simultaneously, yes? Is that stable in flat space? If so, what would occupants experience as gravity? Would it change over time?

if a sphere rotates, it's like multiple currents going around in a circle. I can find the magnetic field of each of those currents at the center point of the circle and add them together. We can integrate with respect to y and R. y ranges from 0 to 5 cm away from the center of the loop and the...

I came up with these: (especially not sure if second is right)

Heya PhysicsForums! Remote Control Car toy tires and wheels. a 4" tire/wheel rotates at 8400rpm at 100mph. Am wondering how many "g's" the tire "experiences" at that rpm; I imagine it being hundreds of times (if below is accurate am WAY off with my guess) Using a centrifugal force...

Hi! My team and i have been stuck in this school project for awhile. Been reading up a lot but can't find the answer. We have been designing and rotating platform that is able to rotate a load of 2000kg. So the rotating platform would something similar to those car turntables where there would...

The Exodus thread got me thinking about swimming pools in a rotating space station. Assume two scenarios: two toroidal pools that circumscribe the station, one is continuous and one is divided into segments by barriers. (Sorry, typing on my phone is very arduous for these old thumbs, so I...

$$I = \int{r^2dm}$$ $$dm = \sigma dV$$ $$dV = 4\pi r^2dr$$ $$\sigma = \frac{M}{\frac{4}{3}\pi*R^3}$$ $$I = \sigma 4 \pi \int_0^R{r^4 dr} = \frac{3*MR^2}{5},$$ which is not the correct moment of inertia of a sphere

Greetings, while studying the stress in the rotating thing ring and find out the last equation that says I would like to understand why? Thank you!

Spectrum of acceleration vs frequency Results of balanced condition Results of unbalanced condition

1) Since the rod is uniform, with mass m and length l, it has a linear mass density of ##\lambda=\frac{m}{l}##, so ##I_{rod_O}=\int_{x=r}^{x=r+l}x^2 \lambda dx=\frac{\lambda}{3}[(r+l)^3-r^3]=\frac{\lambda r^3}{3}[(1+\frac{l}{r})^3-1]=\frac{1}{3}mr^2[3+\frac{3l}{r}+\frac{l^2}{r^2}].##...

Hello, I would like to ask one question. What is the equation for the lift force of a rotating sphere when flying through the air: m = 0.25 g v = 130 m/s angular velocity = 105 rad/s radius = 3 mm air density = 1.2292 kg/m^3 air pressure = 101200 Pa air temperature = 15 °C = 288.15 K If anyone...

The problem says I have a spherically symmetric spinning constant charge distribution of charge Q and angular momentum w; I saw two possible explanations but none of them has made me realize why it is zero, one mentions thata constant w somehow implies a constant E which would mean there is no B...

If a person was rotating on a verticle axis from head to toe like the Earth or quasar. If nothing can go faster than light, from the person's perspective looking at the stars traveling across the night sky, if you increase the rotation of the earth, stars further than a certain critical distance...

two moving and rotating, uniformly weighted disks perfectly inelastic collide. The disks are rotating in opposite directions (see the diagram) At the moment of their collision, the angles between their velocity and the line connecting their centers are 45 degrees. The velocities are therefore in...

Hello! I had a random question while playing around with a garbage can that I hoped y'all could help me walk through: Let's say that I have a hinge on a table, rotating with gravity acting perpendicular to it. Energy is provided into the hinge, let's say by a spring, like so: I want to know the...

Hello all, what would happen to a perfectly conducting cylinder immersed in a rotating magnetic field, with the rotation axis parallel to that of the cylinder? I guess the cylinder would start to rotate with the field? Right? Thank you

* We've a vector ##\mathbf{A}## lying in space, changing according to some rule. * We introduce an inertial frame and find ##\left(\frac{d}{d t} \mathbf{A} \right)_{i n}## in it. * We also introduce a co located frame rotating with ##\mathbf{\omega}##. In this rotating frame I find...

Goldstein 3 ed, pg 171, under" rate of change of a vector " : The author derives the relationship between the change of a vector in a stationary and rotating coordinate system. In the process he uses this assumption :>It is no loss of generality to take the space and body axes as...

Hi, I have a question about hoop stress or tangential force acting within a spinning object such as a solid flywheel. As described in a textbook I’ve seen, the hoop stress tension force acting as if across the diameter of the object, trying to pull it apart, is a resultant of forces acting...

So this is a sketch I made of the situation and this is my approach my approach is incorrect , and Idon't seem to find the mistake , maybe B*p isn't correct. Any ideas?

Assuming no friction anywhere, no drag and perfect inelastic collision Using conservation of mechanical energy i can determine the rotational speed of the rod right before collision occurs. mgh=1/2*i*w^2 center of mass falls 1/2*L so we have: M*g*1/2*L = 1/2*(1/3*M*L^2)*w^2 Solving for w...

I am trying to model numerically the following system: A rigid body mass is rotating freely around an axis (no rotational stiffness/damping) within a range, let's assume plus-minus 3 degrees for now. Case A. The external forces on the mass are low and keep changing which results in the situation...

Hi all, It has been some time since I've done physics. I wish to model some projectile motion of a lure being cast from a fishing rod. The setup is very similar to that of a trebuchet. The fishing rod - we'll assume a perfectly rigid beam - is rotating about a fixed axis. I can calculate...

The other day I found a fascinating video on geometric algebra: At 34:50, after showing how to rotate a vector in three dimensions, he says, "wait a minute, this looks like a spinor from quantum mechanics. The way that spinors rotate is always said to be a part of so-called 'quantum...

The first part of the problem seems easy enough, the free electrons in the wire would move in a circle owing to an electric field that would be induced in the rod which would provide the centripetal force for the same (Please correct me if I am wrong). So we have $$eE=mω^2x$$, where e is the...

Hello everyone, I want to build a rotating display cube (will be mounted on a wall, those cubes that has shops logos ect..), my problem is that I don't know where to start and how to attack the rotating mechanism. I have a 1400Rpm moteur (and it's a 1m per 1m cube that weights around 120kg-150kg...

Hey all, I can't seem to find the answer anywhere, I'm not sure if I'm asking the right question though, if the name or label "Pivot" describes the rotational axis of an object is there a term or label used to describe the outer most point of the rotation?

1) ##LT\sin(\frac{\pi}{2}-\theta)-\frac{L}{2}mg\sin\theta=0\Rightarrow T=\frac{mg}{2}\tan\theta##. ##N_{x}-T=0, N_{y}-mg=0\Rightarrow N=\sqrt{N_x ^2+N_y ^2}=mg\sqrt{(\frac{\tan\theta}{2})^2 +1}## 2) ##E_{k_{fin}}=mg\frac{L}{2}[1+\cos\theta]## 3)...

1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$ 2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this. 3) In ##R_0## the...

The question is simple. The molten stuff inside the Earth will get a smaller volume when it solidifies. Will the Earth increase its rotation speed in reaction to this? What about the magnetic field?

There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...

I have read Classical Mechanics book by David Morin, and there are some parts that I do not understand from its derivation. Note : ## V## and ##v## is respectively the velocity of CM and a particle of the body relative to the fixed origin , while ##v'## is velocity of the particle relative to...

I apologize in advance for any errors in my concepts or assumptions. Feel free to correct me wherever I am wrong. Thanks in advance for the help. There is a vertical shaft which will be operated at around 600 rpm (N) which can be achieved in 2 seconds (or even 4 just an assumption). The shaft...

Hello, reading the wiki entry for Langevin observers on rotating disk - Born_coordinates I'm struggling with the following quoted sentence: But as we see from Fig. 1, ideal clocks carried by these ring-riding observers cannot be synchronized. I do not grasp why, starting from the figure...

Question : Solution attempt : for

So I know Fcp=-m*w^2*r So from the equation -m*w^2*r=m*g*tan(theta) r = r1+r2 so to rewrite -m*(w^2)*(r1+r2)=m*g*tan(theta) So r1+r2=(m*g*tan(theta))/-m*(w^2) r1=((m*g*tan(theta))/-m*(w^2)) - r2 Am I doing this nearly correct?

I want to simulate the time domain data for a rotating radar. I assume that the space around the radar is filled up with a very big extended object and it moves with a constant speed in one direction. Picture attached.I don't take range information here. I am only concerned about the velocity as...

Hello to all members! I'm looking for specific names of 3 mechanical components from the video: Component name 1: min 0:52 from the video Component name 2: min 1:01 from the video Component name 3 (the brake): min 3:53 from the video Perhaps anyone also has a link to the 3 components? I...

Hello, It might sound silly, but when I try to calculate the kinetic energy of a rotating rod to form the Langrangian (and in general), why it has both translational and rotational kinetic energy? Is it because when I consider the moment of Inertia about the centre I need to include the...

Charge will experience a rotating magnetic field around it. What will be electric field ( If any ) at the centre, generated by rotation of magnet ?

Problem statement : We have the graph of the function ##f(x)## shown to the right. The function ##f(x) = \frac{1}{x}## and the domain of ##x \in [1,\infty)##. We have to find the volume and surface area of the 3-D "cone" formed by rotating the function about the ##x## axis. ##\\[10pt]##Attempt ...

hi need help in physics HW: given current density [J][/→]=[J][/0][x][/Λ] and rotating frame with given surface vector: $$ A^→ = A_0(cos(wt)x^Λ + sin(wt)y^Λ$$ in need to calculate I(t) i tried I = ∫J*dA but i don't know i to technically do the math please help me

Looking at L&L's solution to problem four of section §106. Lagrangian for a system of particles:\begin{align*} L = &\sum_a \frac{m_a' v_a^2}{2} \left( 1 + 3\sum_{b}' \frac{km_b}{c^2 r_{ab}} \right) + \sum_a \frac{m_a v_a^4}{8c^2} + \sum_a \sum_b' \frac{km_a m_b}{2r_{ab}} \\ &- \sum_a \sum_b'...

Hi I am working through some notes and came across this example. The wire rotates at angular frequency ω so the polar angle is given by θ = ωt. The generalised coordinate is r. Using the Euler-Lagrange equation leads to d2r/dt2 = rω2 The notes then state that this leads to the solution r = Aeωt...

At first, I inverted the function(##f^{-1}(x)=g(x)##) and calculated the volume through the integral: $$V=\pi\int_{0}^{4}[4-(2-g(x))^2]\ dx$$ but then I questioned myself if the same result could have been obtained without inverting the function. To find such a strategy, I proceeded as follows...

Consider the system of the mass and uniform disc. Since no external forces act on the system, the angular momentum will be conserved. For elastic collision, the kinetic energy of the system stays constant.Measuring angular momentum from the hinge: ##\vec L_i = Rmv_0 \space\hat i + I \omega_0...

Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...

m = 60kg, ω0 = 2.094 rad/s, I of disk = 130 kgm^2 , outer position ro = 1.5m, inner position ri = 0.3m ∴Fifth object : Ffriction = m.ac μ.m.g = m. v^2 / R => vmax = √ 3. (1.5m) . (9.81 m/s^2 ) = 6.64 m/s => ωmax = 4.43 rad/s so when the fifth object move with greater speed than vmax...

Summary:: Please see the attached photo. I have obtained the correct answer, and my solution agrees with the official solution. However, I have some questions about why the solution is correct. (One may have to draw out some diagrams for this problem, it was quite hard to visualise for me.)...