A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.
If an accelerometer is rotating as it moves forward through the air, what force is acting on the accelerometer? Say we remove gravity and just concentrate on the horizontal axis.
I know there is centripetal and tangential acceleration that shows up as an offset in the sin wave, but what causes...
Hi there,
The settling velocity is terminal velocity at which drag force is equal to the gravity. When the sphere is in rotating field the terminal settling velocity is reduced. What will be the expression for it in rotating field?
Hello! Is there any work which looks at the frame dragging effect due to a rotating quantum object (e.g. in an eigenstate which is a spherical harmonic)? I would appreciate any reference on that.
I tried to solve the problem like this.
4-1. m d/dt (v_1) = mg sin(theta) - F
4-2. m d/dt (v_2) = R - mg cos(theta)
If there is no slip, v_1 = v_2 = 0, so
F= mg sin(theta), R= mg cos(theta).
In the rotational motion equation, we intergrate
5-1. I omega^2 = 2dmg ( sin theta_f -...
Hi!
I am a high school physics teacher in Korea.
I have a question for you, a physics expert.
A rod that falls while rotating from the end of a table
A rod of mass m and length L is inclined by theta o (thera_o > 0) when the center of the rod is in contact with the end of the table, and the...
If I understand the problem correctly, I need to find the angular frequency of the mass's oscillations about the radius R, which, I think, should be the length of the spring when the mass is merely rotating with angular speed ω (and not oscillating along the radial direction). I was able to find...
Hello a group of students and I are trying to design a car with a wingnut breaking mechanism. However instead of the wingnut hitting the washer connected to the wood and stopping the threaded rod from rotating the threaded rod and wheels actually shift left while the wingnut stays stationary...
So I tried it out by taking a patch of area da at an angle theta from the x axis and rotating it around the axis, this gives you a cone whose, locus is that of a uniformly charged ring since all of the area is at the same angle theta and the surface charge density varies with theta.
My solution...
My answer is (B) but the answer key is (A).
My working:
$$\varepsilon=-\frac{d\phi}{dt}$$
$$=-AB\frac{cos\omega t}{dt}$$
$$=AB\omega \sin \omega t$$
Why the answer is zero? I thought the flux will be zero, not the emf.
Thanks
Ich wäre Ihnen sehr dankbar, wenn Sie sich meine Lösung der folgenden Übung ansehen:
A sphere with radius ##R ## is spatially homogeneously loaded and rotates with constant angular velocity ##\vec{ \omega}## around the ##z ## axis running through the center of the sphere.
Calculate the...
Hi,
In David Morin's "Introduction to classical mechanics", Problem 6.8, when deriving Hamiltonian of the bead rotating on a horizontal stick with constant angular speed, the Lagrangian derivative over angular speed isn't included.
Why is that?
Specifically, the Lagrangian takes form...
So I have a system in which there is a disc with a moment of inertia of 1248.68. this system can rotate this disc from zero RPMs to 36 RPMs and approximately 2 seconds. How would I go about determining how much power is exerted to do said work? Many thanks
Usually, I like to take a physical approach to phenomena that occur in everyday life. But I feel difficult to solve problems because I don't have higher education
My question stems from this question (What's the difference between running up a hill and running up an inclined treadmill?), which...
Forces on rotating disk object
Hi. Is it convenient to ask following question.
Suppose we have solid circular object and 5 different moments
like in the picture:In moment 1 we apply force (downwars direction) so as to start rotating the object around center of
the mass (green dot) , Only...
I believe I've solved this problem, however, I got through it pretty quickly and since it's the last problem on the assignment, I feel that I may have had an oversight.
For part a, I got: fs=md(α^2)(t^2)
and for part b, I got: ω=Sqrt((µs*g)/d)
Could someone confirm my answers? I've attached a...
For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...
Dear People,
I have a question. I have a rotating tube like a line that has two end and one of them is the center of rotation (like a watch arrow just tube), and inside the tube a mass that is moving towards the center of rotation. So the masses moving along the line aka along the length of the...
The cylinder in question would have a moment of inertia of ~1.67kg*m² and rotational KE of 2.058J. At the point of impact also, assuming the body hits the sphere at a 90deg angle after traversing 90deg of displacement, it should(?) exert a force of 1.31N - enough to give an acceleration of...
When a Kerr black hole evaporates, what will the Kerr parameter do?
Stay constant at initial value?
Approach zero?
Approach unity?
Approach a target value somewhere between zero and unity?
Also, Nordström black holes in practice (with matter around) would have a strong tendency to attract...
there are a bunch of problems in this section that ask similar questions, but they ask the amplitude and this doesn't. this is an even problem so i do not have the answer, but my hunch is that it is not an amplitude question. i solved for the amplitude so i am guessing i got this one wrong...
Hello all, I am currently studying for a physics a-level qualification in the UK, I use the AQA specification and I am having trouble understanding this image representing a scenario I found in my textbook. The first image in the three part diagram shows this rotating coil and to me, it makes...
Hey folks,
I've been looking around but can't piece this together as there are more than one equation and variable to take into account.
My situation - I have a pmma material disc on an axis , the center hole (axis hole) is 20mm wide so a radius of 10mm, while the outer edge is at a radius of...
Hello! I have a radially pointing electric field i.e. at a given radius, R, the electric field has the same magnitude and points radially around that circle of radius R. I have a particle moving around that circle of radius R, with uniform velocity (ignore for now how it gets to move like that)...
My issue is in deriving the coordinates of a point on a wheel that rotates without slipping. In Morin's solution he says that:
My attempt at rederiving his equation:
I do not understand how the triangle on the bottom with sides indicated in green is the same as the triangle on top that is...
hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...
The Bell inequality requires three conditions, A, B and C that can have two values (pass or fail, say). In the Aspect experiment A defines a plane, B a plane of A rotated by 22.5 degrees, while C is A rotated by 45 degrees. We take joint probabilities, and two are A+.B-, and B+.C-, and from the...
Hello! Assume I have a 2 level system, where the 2 levels have opposite parity. If I apply an electric field, I will get an induced dipole moment. For now I want to keep it general, so the induced dipole moment can be very large, too. Let's say that I start rotating this electric field in the...
I'm having some trouble figuring this problem out. I've found the tension in (a) but I don't know where to start with (b). I've found that the distance between one of the masses and the rotational axis on the picture is R+0.52 m and that the masses rise to a height of h = 0.3 m.
The moment of...
Hello everyone, I am Abheer and I am a high school student. Few days back I saw an article about RDEs (Rotating Detonation Engines). The article said it is the future of aviation propulsion. I want to ask, is it really so that RDEs are future or the low/high bypass turbofan engines will continue...
As can be seen below we have 3 ring magnets. The middel one floats in between the other two. We want to know how to calculate the air friction of the middle ring magnet if this rotates.
Hello, I am trying to figure the strength (in lbs) of a strap needed to attach 2 Rolls together without breaking. Each wheel has a weight of 1000lbs and a diameter of 30in. If there is required information missing, let me know.
My current spaceship design with several ring habitats (6 in my case) works well for worldbuilding purposes, in the sense that the reader should easily be able to tell what types of facilities can be found where on the ship. That’s because the rings distinguish themselves from each other by...
Ok. I was writing a big text about it, but i will summarize it.
We know that $$P = \frac{\mu \ddot{m}^2 w^4}{12 \pi c^3}$$
We know, as well, that $$\nabla \times M = 0$$.
Also, $$\vec K = M \times \hat \rho = M \hat \phi$$
Total current, I = $K l = M l$.
Magnetic moment, so, $$M l \pi r^2...
Hello everyone!
So I've been studying gyroscopes, and see that a torque about the shaft alters the momentum, we can find the new momentum vector by finding the torque, multiplying by a small amount of time, and finally adding that vector to the momentum vector. This will create a precession for...
Video:
I recently happened upon this holographic display design where a number of blades with led strips affixed rotate like a fan. It quite puzzles me how this such a design achieves the desired results. I am pretty confident that they use polar coordinates when mapping the pixels, but I am...
In general relativity, rotation of mass gives rise to framedraging effects, just like linear motion does, because of the off-diagonal components in the mass-energy-momentum tensor. So around Bonnor beams there is framedragging, as well around a rotating mass.
Now imagine a spherical rotating...
From the top of my head, I would say that yes, the very moment our clocks are aligned, and the two bullets are launched it is perfectly ok to use the relativistic velocity addition formula to determine the speed of the bullets from my reference frame. But the more the disk keeps rotating, the...
To solve this problem, we need to evaluate the following integral: $$\epsilon = \int_{P}^{C} (\vec v \times \vec B) \vec dl$$
The main problem is, in fact, how do we arrive at it! I can't see why a Electric field arises at the configuration here. The magnetic field of the rotating sphere is...
Summary: Consider a body which is rotating with constant angular velocity ω about some
axis passing through the origin. Assume the origin is fixed, and that we are sitting
in a fixed coordinate system ##O_{xyz}##
If ##\rho## is a vector of constant magnitude and constant direction in the...
Query - does a centrifuge spinning to create X g-force, mounted on a platform that is rotating the the same rpm's the opposite direction, negate the g-force? Or does the g-force stay the same but from an outside perspective the centrifuge appears stationary?
Obviously, a third observer who is at rest with respect to the disk will see that the clock on the outside has a much faster velocity than a clock on the interior of the disk, so clearly the outside clock will show that it has measured less time.
But that's one question. What about looking at...
In optics experiments, I often see the following optics configuration to rotate the polarization of an incident linearly-polarized laser beam. The final reflected beam has its polarization rotated by 90 degrees. My question is:
1) Between the quarter plate and the mirror( reflecting surface)...
Hello guys, I'm a newbie.
So I have developped an application that rotates a cube using quaternion.
The initial values of the quaternion are ( w=1.0, x=0.0, y=0.0, z=0.0).
Now I want to apply two consecutive rotation using two different quaternion values:
The first rotation corresponds to...
If I'm correct then the maximum change in magnetic flux occurs when the semi circle crosses the point at which it's plane is parallel with the magnetic field and minimal when it crosses the point at which the magnetic flux is maximum ( perpendicular with the field). I'm having trouble writing a...
Picture a flat disk of radius r with a radial vane. The disk is rotating at angular velocity w. Assume the vane is straight, starts at the center and ends at the perimeter of the disk.
A very small round mass ( of m grams) is dropped onto the disk very near the center. The vane contacts it and...
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?