Rotating Definition and 1000 Threads

Let $R$ be the region $\left\{(x, y) : 0 \leq x \leq 1, 3^x − x − 1 \leq y \leq x\right\}$. Find the volume of the solid obtained by rotating $R$ around the line $y = x$.

Quick question about the relativistic energy of a rotating thin ring, hoop or cylinder. Is there any reason why the relativistic energy would be anything different than ##E=\gamma_t m_0 c^2## where ##\gamma_t## depends on the tangential velocity ##v_t## observed by someone at rest with the...

is this eqn correct

I have a disc. The center of the disc is its center of mass and the motion of the disc is purely rotational (no translation). What is the angular velocity in the center of the rotating disc?

I first calculated induced emf and then calculated torque about O.But what will i do further.I think i need to find current and then fidn emf=IR. Help please.

There are two points of the smaller disck such that a line is tangent to the two discks and passes by that point. If the particle leaves of any point belongin to the arch that connects these two points, then it will hit the other disck. So I managed to calculate the value of this arch and divide...

I tried making the fbd of both blocks the block on the incline will have mgsin30 friction force, tension and centrepetal force's cos component similarly second block will have mg tension and friction where normal will be centrepetal force after solving my ans is not matching

Let's say I can see a star in a distance of 1ly in front of me. I'm sitting on an office chair and begin to rotate with a speed of 1/s (1 rotation per second). Then I consider me as not rotating and everything else as rotating. Now I will see the star traveling a circular path with the...

I was able to find the equation of an ellipse where its major axis is shifted and rotated off of the x,y, or z axis. However, I could not find anywhere an equation for a spheroid that does not have its axis or revolution along the x,y, or z axis. How might I go about deriving such an...

What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors ##\mathbf{ \hat{r}}## and ##\mathbf{\hat{\theta}}## have a variable direction, such that for a Cartesian coordinates system's base...

I'm tasked with drawing the trajectory of the Moon around the Earth (in 2D), taking into account the fact that the trajectory also undergoes precession, so the elliptical orbit rotates about it's center (I think it should rotate around the Earth-Moon barycenter, but for the first step I...

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I want to make a small mechanical calculator with no electric parts, nothing too advanced but a few binary gates capable of some basic functions. All the examples I were able to find were amazing but were still dependent on electricity to drive the mechanism. One possibility is a spring but I...

The motor is required to operate at its resonance frequency and I am looking to add a thin-walled (0.010") copper tube inside the stator bore to add some damping. The current motor air-gap is 0.015". If I install a copper tube in the stator bore bonded to the stator and leave a 0.005" air-gap...

Consider a wagon with length L and constant speed v on the straight part of a rail. The wagon has clocks on both ends that are sync in the co-moving frame (of the wagon and the clocks). Then there is a curve in the rail with radius r. The speed of the wagon in the curve is still constant v, but...

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.

Bolt comes out by distance d=1.58 mm when speed of rotation of shaft reaches its trip value (w_trip). m is mass of trip weight (Bolt assembly) One of the approach which I had considered is work energy theorem. Initial energy = 0.5m*(w_trip*(r+d))^2 Final Energy= 0.5m*(w_trip*r)^2 (Assuming bolt...

As shown in figure there's a homogeneous solid sphere. It is rotating about axis which is passing through point P directed perpendicular to the plane of paper. (In short like a pendulum). I'm neglecting gravity and assuming a force F which is directed perpendicular to the string. (The string...

Starting from this post, we are able to define the concept of (proper) acceleration or rotation without any reference to something else About this definition which is the physical meaning of gyroscopes axes pointing in three mutually orthogonal spacelike directions ? In other words, from a...

I tried asking a similar question in cosmology but got no answer there so here goes... Suppose I am on a windowless spacecraft in the middle of an intergalactic void. I know that the spacecraft is spinning from measuring the centrifugal forces but have no way of observing the outside...

I have a frame which supports a crank rotating through 360°. The crank lifts a 30 kg weight 540 times a minute ( 540 rpm). As the crank moves 0° to 90° the weight is accelerated to full speed which means it has thrust but then from 90° to 180° it is slowed to a stop then from 180° to 270° it is...

I used the above equations to solve for tension, torque, inertia, and angular acceleration. Are the formulas I used correct for the given system? How can I calculate Inertia from the trendline equation, I'm drawing a blank.

I have a question about a rotating vector field: if there is a vector ##A^i(t_0)## at the origin in coordinate space ##IR^3## , when ##t≥t_0##, the vector rotates with a changing angular-velocity ##ω^i(t)##. then we can get a rotating vector field ##A^i(t)##. then how to describe ##A^i(t)##...

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...

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...

Homework Statement Calculate radius of rotating wheel. Linear speed of point "a" (red dot) is 2.5 times faster than linear speed of point "b"(blue dot) that is 5cm closer to center of wheel. Right answer is 8.33cm. I drew a sketch without linear line. Homework EquationsThe Attempt at a...

<< Mentor Note -- Two threads on the same question merged into one thread >> How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades? Example, when it falls vertically to the blades, it's Pmax= 8/27Sρu13 But if there's for...

hello, i have a doubt i bought some small neodimium magnets 8x3mm and now i would like to try some experiments with them i have a doubt: if i rotate one of these magnet around one of its parallel axis, very fast , near 1000000 rpm, what happens to the magnetic field produced by the magnet? if...

Homework Statement Acceleration experienced by an astronaut in a rotating space station. Homework Equations What force would he experience is his own rotating frame of reference. The Attempt at a Solution Newton's second Law for a rotating frame is: mr'' = F net+ Fcor + Fcf Fnet (In the...

Statement of the problem : Two ice skaters circle about a point while holding hands. At a certain moment both let go and move along straight lines. Are the two straight lines parallel? Explain. My attempt : Calling the two ice skaters ##S_1## and ##S_2 ##, they must lie...

We are aware of the well-known problem of a rotating physicist whose angular velocity ω increases as a consequence of angular momentun conservation (##I_1 \omega_1 = I_2 \omega_2, \Sigma \tau_e = 0##). I am assuming that the net external force (##\Sigma F_e##) is also zero along with the net...

Homework Statement A 40 cm rod is rotated about its centre inside a region of uniform magnetic field of 6.4 T. Given that the speed of rotation is 15 rad/s, find potential difference between the centre and either end of the rod Homework Equations emf = - ΔΦ / Δt ω = 2π / T The Attempt at a...

Homework Statement We have a ball of mass ##m##and radius ##r##. it is placed on an incline (We don't know the angle of the incline, nor we do whether the angle is constant along the incline - maybe it is a curved incline) and then released. The COM of ball is ##h## meters above the incline at...

1. A closed cylindrical vessel filled with water (at room temperature) contains a small air bubble of normal pressure and volume ##V=1~{cm}^3## inside in it.The cylinder is then started to be rotated slowly with a small angular acceleration in a complete weightlessness (at a space station)...

The problem: a coil of radius r, length l and N turns, rotating with constant angular velocity ω around an axis perpendicular to its simmetric axis and passing for the center of the coil. The coils is submersed in a static magnetic field, intensity B0, perpendicular to the axis of rotation of...

Homework Statement [/B] A train stands in the middle of a rotating disk with an initial angular velocity of $\omega_i$. The mass of the train is m and the moment of inertia of the train-disk is I. At one point the train departs on a straight track to a distance R from the disk's centre. (R...

Hello all! I just discovered PF as I have been searching about a project I have been pondering for a day. The idea is to have a device that I can set my 3lb camera and have the device rotate left-to-right && || right-to-left over the duration of 2 hours for use in a sunset/cloud timelapse...

Hello, As many know, when an external force acts on a rigid body and the force's line of action does not pass through the body's center of mass ##c.m.##, the force will cause the body to both translate and rotate exactly about the ##c.m.##. Otherwise, the body will solely translate without...

Is there a way to calculate the vibrations on a shaft rotating at a certain rpm? Is there a way to accurately simulate this?

Is the equation presented (that the time-derivative of a given vector in such a scenario is equal to its angular frequency vector cross the vector itself) true in the case of a vector whose origin is not on the axis of rotation? The way I'm visualizing this, if we take such a displaced origin...

Homework Statement .A cylinder P of radius rP is being rotated at a constant angular velocity ωP along positive y-axis with the help of a motor about its axis that is fixed. Another cylinder Q of radius rQ free to rotate about its axis that is also fixed is touched with and pressed on P making...

I tried to calculted the rotating speed fro a proton from the clasical point of view by using its magnetic moment and the moment of a rotating sphere uniformly charged as example here: https://ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/exams/MIT8_07F12_quizsol2.pdf It is said...

I have a ball of mass m that is situated on horizontal plane on the northern Hampshire. I am asked to show that the ball is moving, clockwise, in a manner of r = v / ( 2Ω*sin(λ) ) where v is the ball's velocity, Ω is Earth's angular velocity, and λ is the terrestrial latitude So here's what...

Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...

I have a disc that is rotating due to air being blown at its outer radius. The incoming relative velocity of the air is high, therefore the effect of friction supersedes the effect of conservation of angular momentum. The tangential portion of this velocity decreases due to the friction as it...

If talking about a particle rotating around an axis away from it by r. if the particle is moving with constant angular velocity ω. is the linear velocity constant or no? Now what I know is that since we have Vt= ωr, so r doesn't change, as well as ω, so Vt is said to be constant. but I think...

It is often proposed that gravity could be simulated on a space station by rotating around an axis, such that the astronaut experiences the centripetal force of the space station wall, analogously to gravity. It is usually mentioned that the radius of rotation must be very large to avoid...

If one rotates a tangent plane on a curved surface, this point can be expressed as follows: x' = x cos(theta) - y sin(theta) y' = x sin(theta) + y cos(theta) One solves for x and y and computes based on the deviation of the deviation. My question is: would the answer differ if you choose a...

My problem reads as follows: Point p=(3,3√3) is rotated counterclockwise about the origin by 75 degrees. What are the coordinates after this rotation? I have no idea how to rotate a point, let alone by 75 degrees.

1. Homework Statement I want to calculate the rotational period and surface velocity of a Bishop Ring with a radius of 80 km and a surface 'gravity' of 0.86 G I should note that this isn't for homework. It's for personal interest. I'm looking for a sanity check on this. The homework forum...