Rotation Definition and 1000 Threads

http://im54.gulfup.com/ZtJZd5.png http://im54.gulfup.com/SJgJXh.png Till now compared with other subjects that I studied by my self, linear algebra is really the toughest one :bow: Anyway, here I found a plane using characteristic eq. which really surprised me since det(M)=1, M is the matrix...

Hi everybody, This is my first post, so I apologise for all the possible mistakes that I can make now and in the future. I promise that I'll learn from them! My question is the following: It's well-known the relationship between two pair of cartesian axes when a circular rotation is made...

I am interested in this. I'm looking for a simple answer and a more in depth answer (if possible). Any links regarding the math behind it would be great. Thank you.

Homework Statement A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. Model it as a stiff rod of negligible mass, 3.00 m long, joining particles of mass m1 = 0.120 kg and m2= 60.0 kg...

Hi. I am confused about something and it is making me feel rather stupid. First of all i will explain what i know. I know a solar day is 24hrs long and it is defined by the position of the sun. I also know a sidereal day is 23h 56m and is defined by the postition of the stars (basically)...

How does the atmosphere rotate with the Earth on its axis? There are no forces acting on it that would be strong enough to keep it moving with the ground. Gravity acts perpendicular to the direction of rotation, so it would not be able to cause this motion. It would only be able to keep the...

Hi guys, I am new to the forum and I have what is probably a simple question for most of you. Unfortunately a great deal of people I know have suddenly taken up the idea of a "Flat Earth", and they consistently post things that try to contest that a flat Earth is a far more logical idea than a...

Hello. Suppose I have a coordinate system with the origin at the center of mass at rest of some rigid object and I wish to calculate the total change in angular momentum of the object with respect to it's center of mass. If I apply a torque to the object, that also happens to be an unbalanced...

I set up an experiment where I drove a solenoid with an H-bridge circuit at one voltage, and then I repeated the experiment with a higher voltage. There was a magnet positioned above the solenoid such that it was free to oscillate side to side (see picture). My observation was this: with the...

Why does tension across a rod rotating horizontally vary when it is rotating about one end?

Hello! While studying from the book 'Fluid Mechanics' by Cengel I came across the section which explains the behavior of fluids acting like a rigid body when the cylindrical container which contains the liquid rotates with a uniform angular velocity. Without much explanation the author states...

Homework Statement Let ##U## be a ##2\times 2## orthogonal matrix with ##\det U = 1##. Prove that ##U## is a rotation matrix. Homework EquationsThe Attempt at a Solution Well, my strategy was to simply write the matrix as $$U = \begin{pmatrix} a & b\\ c & d \end{pmatrix}$$ and using the given...

Hi, I have a 3d space with metric ds^2= -r^a dt^2 + r^bdr^2 +r^2 dy^2 and I need to construct an orthonormal frame. The first of these three basis vectors is fixed, let's say as e_0=A \partial_t + B \partial_r + C \partial_y To find the other two I set v_1=\partial_t, v_2=\partial_r and...

I think I'm having a really big block over a really small hangup, so forgive me. I'm on an internship and this is my first time working with rotations/change of basis in a real world scenario. I'm creating a calculator that gives torque in a door mechanism, after a given roll and pitch of the...

Check out this one... https://www.facebook.com/groups/jeephysics/permalink/860646844004924/

Hello everyone! I am trying to write an app that needs to be able to tell if a vehicle is accelerating or breaking. In this sense I used the accelerometer in the phone. At the moment I managed to isolate and subtract the gravitational pull of the Earth from my readings and I am using a noise...

This is the kind of gyroscope that I am talking about: Where did the kinetic energy of precession come from? The gyroscope's spinning angular inertia? If so, how does it transfer into the precession? Is a torque applied horizontally (along the x-y plane) when the system is under the effect of...

I am reading a paper and am stuck on the following snippet. Given two orthonormal frames of vectors ##(\bf n1,n2,n3)## and ##(\bf n'1,n'2,n'3)## we can form two matrices ##N= (\bf n1,n2,n3)## and ##N' =(\bf n'1,n'2,n'3)##. In the case of a rigid body, where the two frames are related via...

I understand the right hand rule and the equition, but why is the direction of the torque perpendicular to the force on the counter clockwise side of the force and crossing the rotational point?

If I have a magnetic setup in frictionless, etc. area as follows: N / / / ---------------------S Will the "south" pole rotate up to the "north" pole, causing the system as a whole to rotate?

Homework Statement Taking moment about A , the mass of 2.0g and 0.50g is rotated in the clockwise direction is because they are both directed in downwards position ? while R2 is acted in upward direction , so it is rotated in counter clockwise direction ? Taking moment about G , why R1 is...

Is anyone interested in telling me the force created from 2 propeller blades rotating 2000 rpm.The total diameter of the prop is 72 inches and the weight of 1 blade is 4 lbs. Reason for the question is I want to mill a clark-y profile the length of the blade less ,4 inches for a bolted...

Homework Statement A lever with one end on a pivot point, a point mass on the lever's shaft with a certain arm length (d), it is also the only relevant mass body (m). A torque (Tauapp.) is applied to the lever, an angular acceleration (alpha) transpired. Find the relationship between the force...

I watched an interesting video on YouTube by veratisirm where he had a meter long metal rod with a huge metal fly wheel on the end of it. Long story short he could barely lift the thing but under full spin he could just about swing the thing like a sword. the only thing was the precession wanted...

Hi Folks, I calculate the eigenvalues of \begin{bmatrix}\cos \theta& \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} to be \lambda_1=e^{i \theta} and \lambda_2=e^{-i \theta} for \lambda_1=e^{i \theta}=\cos \theta + i \sin \theta I calculate the eigenvector via A \lambda = \lambda V as...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] Hello, I have a problem with rotation matrices, its just a comparison problem. Θ must be 240 or -120, I don't know how the book show the answer like that, these are the two matrices...

Where from do the electrons in an atom get the energy to keep constantly moving around the nucleus of an atom

Hello, This problem has probably been done before in different guises but I am struggling, and hoping for help. I am struggling to understand a phenomena which I am assuming is one and the same: Equatorial Bulge of the Earth Flat Plane in which the Planets rotate Protoplanetary disks are flat...

Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's...

Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin. Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move...

It seems that combining two Lorentz boosts cause rotation: https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer...

Homework Statement Two identical disks with mass m and radius r are connected via a massless wire of length L which is winded up around both disks. Disk B is connected to the ceiling and is free to rotate around its axis. Disk A is besides disk B and will fall due to the gravitational force...

I am interested in whether it is necessary to account for the effects of the Hubble Redshift in determining the rotation velocities of galaxies exhibiting keplerian motion and, in particular, whether the associated spatial expansion of the Universe is known to result in spectral shifts that...

Consider the rotation group ##SO(3)##. I know that ##R_{x}(\phi) R_{z}(\theta) - R_{z}(\theta) R_{x} (\phi)## is a commutator? But can this be called a commutator ##R_{z}(\delta \theta) R_{x}(\delta \phi) R_{z}^{-1}(\delta \theta) R_{x}^{-1} (\delta \phi)##?

Hello buddies, Could someone please help me to understand where the second and the third equalities came from? Thanks,

I have some questions about acceleration that I'd like for someone to explain to me. As far as I know, acceleration depends on either change in velocity or change in direction (or both). So if I'm going 1m/s North constantly I'm not accelerating. However, what would be the acceleration if I walk...

How interplanting and crop rotation helps to control the pethogenic diseases and parasitic weeds and also explain what are parasitic weeds ? What is crop rotation ? What is interplanting ? Thanks :-)

Homework Statement Homework Equations ##v = r \omega ##?? The Attempt at a Solution The answer is 0...why?

Hello Everyone, Let us think about a rod whose length is L and end points are A and B. The road is parallel to the ground therefore the weight of the rod is perpendicular to the line between A and B. The weight of the rod is F and two forces with the magnitude of F are exerted on both ends and...

Homework Statement See Diagram Homework Equations See Diagram The Attempt at a Solution I have been looking for hours for the correct formula but do not know what to use or where to start. If you can point me in the direction of the right formula if one is needed, and I would be very...

It would seem to me that if you fly from point a to point b following the rotation of the earth, you'd have to go faster than this rotation to move forward. For example, if the Earth spins at 1,040/mph, then wouldn't a plane have to go faster than this just to escape the spin of the earth? I get...

I'm working through Meisner Thorne and Wheeler (MTW), but have been temporarily sidetracked by a problem with rotation matrices. I've worked through the maths and produced the matrices by multiplying the three individual rotation matrices, (no problem there) but I have been trying to work out...

Homework Statement An area is enclosed by y=1/x, the positive x-axis and x=1 and x=2. Determine the volume of the rotational body that is created around the y-axis. Homework Equations The formula is pi*integrate from d to c for x^2 dx. The Attempt at a Solution Take a look here...

Homework Statement The curve y=1/x and the line y=2.5-x enclose an area together. Determine the exact volume of the rotating body that is formed when this field rotates about a) The x-axis and b) The y-axis Homework Equations The formula for rotation around the x-axis is pi*integrate from b to...

Homework Statement An aeroplane loops the loop in a vertical circle of radius 200 m, with a speed of 40 m s^-1 at the top of the loop. The pilot has a mass of 80 kg. What is the tention in the strap holding him into his seat when he is at the top of the loop? Answer: 160 N. Homework...

Homework Statement There is a point P(x,y) and now I rotate the x-y axis, say by θ degree. What will be the coordinates of P from this new axis. I have google but found formula for new coordinates when the points is rotated by θ degree. So I tried my own. So is there other simplified formula...

The Feynman propagator is $$ G_{F}(x) = \int d^4p \, \frac{e^{-ip x}}{p^2 - m^2 + i\epsilon}. $$ I want to understand why the directions of Wick rotation in position space and momentum space are contrary. Every book I find says something like "we should keep ##xp## unchanged", but why? As we...

Homework Statement A body is suspended on a spring balance in a ship sailing along the equator with a speed ## v' ## . If ## \omega ## is the angular speed of the Earth and ## \omega_0 ## is the scale reading when the ship is at rest , the scale reading when the ship is sailing, will be very...

Homework Statement Homework Equations a=Rα The Attempt at a Solution Free body diagrams: For larger pulley, TR=Iα ⇒ T=½MRα If this pulley rotates by some amount suchat x length of rope becomes free, and if I hold the smaller pulley at rest, then this extra length of rope comes bellow the...

Homework Statement Two hoops are fastened together as shown below. Smaller hoop mass m, and larger hoop mass 3m. The system is now placed on the table and the system is released from rest in the position shown below. There is sufficient friction between the large hoop and the table so that it...