Rotation Definition and 1000 Threads

So my co-workers and I have had a dispute after hearing a podcast on NPR about Earth's rotation. One question was about what would happen if one side of the Earth always faced the sun (tidal locked) and another question was about what would happen if the Earth stopped rotating. From what I've...

Hello, I have a few questions about rotation and relative motion. Suppose we transport the proverbial spinning ice skater used to demonstrate conservation of angular momentum to beginning physics students to a universe with only her and two planets. She is now spinning in deep space...

It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...

It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...

If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R is this expression correct? (When ball reaches lowest point) ##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2## where...

Homework Statement A spaceship in outerspace has a donut shaped with a 500 m outer radius. The inhabitants stand with their heads towards the center and their feet on an outside rim. Over what time interval with the spaceship have to complete one rotation on its axis to make a bathroom scale...

Homework Statement A red Archimedean spiral is fixed to the ground. An external motor turns a grey support clockwise at w, the support can only turn around itself. On the support there is one orange disk that doesn't turn around itself at start. A stem is on the support. That stem: - turns...

I'm an Arduino electronics hobbyist I'm not a professional electrical engineer. How would I mount a small ultrasonic sensor on a continuous rotation servo, without tangling the wires? How would I fix this problem easily and what's the most common way to mount electronics in a rotating object...

I understand the Kerr metric has an off-diagonal term between the rotation and the time degrees-of-freedom? That a test mass falling straight down toward a large rotating mass from infinity will begin to pick up angular momentum? Is that what’s called “frame dragging”? Did the Gravity Probe B...

I noticed that if you swing a ball around attached to a string with a centripetal force. The ball also rotates. What causes this rotation? Is there always rotation when there's a centripetal force? does an object orbiting the Earth always face the same way as it orbits?

Does spin for particles actually refer to spin as in rotation? Or does it mean something else. Do all elementary particles rotate? Without a magnetic field can you have rotation or does the rotation create the magnetic field?

On the website http://www.real-world-physics-problems.com/physics-of-billiards.html they take this equation ∑Mg = IG∝ where ∝ = -agx/r for the rotation of a rigid body where there is no slipping They then change the equation to F⋅(h-r) = IG(-agx/r) why is ∑MG = F⋅(h-r) when ∝= -agx/r?

Homework Statement If arg(\frac{z-ω}{z-ω^2}) = 0, \ then\ prove \ that\ Re(z) = -1/2 Homework Equations ω and ω^2 are non-real cube roots of unity. The Attempt at a Solution arg(z-ω) = arg(z-ω^2) So, z-ω = k(z-w^2) Beyond that, I'm not sure how to proceed. Using the rotation formula may also...

So, I'm working on my semester finals for my high school physics class, and I've run across a problem that has me stumped. I've included the pertinent material below. Homework Statement A rocket with a mass of 2kg and traveling at 14,008.34 meters/second loses 10% of its velocity as finishes...

Homework Statement I changed the problem, because I understood my error I forgot a force. It's the same problem with one motor. A motor drives two disks on a support. The support is turning clockwise at w1. Disks turn at w at start. The motor M gives a force F and a counterclockwise torque...

what is the cause of the centrifugal force from the perspective of the rotating observer? Also is rotation relative like linear motion?

how do we know which system of coordinates to use whether (polar) or (tangential and normal) in case of a rotating system ??

If you throw a ball obscenely high (ignoring air resistance, etc), and the Earth is rotating, the ball will land in a different spot. Relative to an observer on the Earth, the ball has a sub-orbital trajectory across the surface. If we attach thrusters onto that ball, and have it burn at its...

Homework Statement Hi all, There is a question from the course book: Homework Equations S=k_B ln W The Attempt at a Solution My solution: So first of all, for each molecule, there are 2 motions: translational and rotational. For rotational I get: W_1 =\Omega \left ( \theta \right ) For...

Homework Statement A yo-yo is pulled with a constant tension T. The string is horizontal and parallel to the table and unwinding from the bottom of the spool, as shown. The yo-yo's outer radius is R and the spool radius is r. The mass of the yo-yo is m and the moment of inertia of the yo-yo...

Homework Statement A solid sphere of mass M and radius R rotates freely in space with an angular velocity ω about a fixed diameter. A particle of mass m, initially at one pole, moves with constant velocity v along a great circle of the sphere. Show that, when the particle has reached the other...

Many apologies in advance if this question is ridiculous or if it has already been answered on another thread. I've searched and searched through the forums and haven't found the answer - please do direct me accordingly if that's possible. If not - please help! Preamble: We know from...

I'm reading Halliday's chapter or rigid body rotation. In the derivation of Newton's second law for rotation, it is assumed that the object is hinged about some axis ( the connection would be a frictionless pin). The law is derived for such a connection, but is later applied to objects that...

Can anyone explain how these two particles actually a complete molecule (given in the image)will rotate about x-axis?

I think I more or less understand how a gyroscope precesses--at least mathematically and in terms of torque/angular momentum. My question here is: how does the gyroscope start precessing in the first place? The external forces on the center of mass are entirely vertical. Given that Newton's...

Hi, I would like to study these two cases: Case A 1/ I turn counterclockwise the ring at w2, this need the energy \frac{1}{2}mr^2w_2^2 with m the mass of the ring 2/ I turn the ring with arm clockwise at w1, this need the energy \frac{1}{2}md^2w_1^2 with d the length of the arm 3/ I eject...

Homework Statement Suppose two spherical balls roll down a hill without slipping. If both are released from rest, which one will roll the fastest? The answer is that both will roll at the same speed, even if they are of different sizes and weights, but I do not understand why Homework...

Hi What is the cause of aerospace rotation whit the earth? May the gravity haves any roll?

Consider this: We have a sphere rolling down a slant, released from some height h with null velocity. At the end of the slant its potential energy will have been fully converted to kinetic energy, part translational and part rotational. Now consider this: at the end of the slant the ball enters...

[FONT=PT Sans]I have an inertia tensor D in the old Cartesian system which i need to rotate through +90 in y and -90 in z to translate to the new system. I am using standard right hand rule notation for this Cartesian rotation. [FONT=PT Sans] [FONT=PT Sans]D=...

Today in class we learned about how if a force F is applied to a dumbbell on its center of mass and then separately applied to the edge where it gets its maximum torque, the dumbbell will have the same CM velocity after. It makes sense when you think about it in terms of momentum. F times T...

Dear all, In textbooks about optics in magneto-optic materials, we often come across a Hermitian permittivity tensor with off-diagonal imaginary components. These components are relevant to the Faraday rotation of plane of polarization of light through the material. Now my question is: Is the...

I've spent at least an hour trying to figure this out, but can't seem to figure out how to solve this. 1. Homework Statement A 170g , 30.0-cm-diameter turntable rotates on frictionless bearings at 66.0rpm . A 25.0g block sits at the center of the turntable. A compressed spring shoots the block...

Hello, I've been reading astronomy books for some time now but after leaving things for a while I seem to forget rotation directions. For example, I know that the Earth spins in the anticlockwise direction. That is easy to see why. They say that motion of the Earth is eastwards. Because of the...

Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...

As the title says, can there be any rotation if only one force is applied to an object at rest. For instance, if I had a rod laying flat on a frictionless surface, and I pushed one end, am I correct to say that Newton's second law says that all of that force goes into acceleration the center of...

Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...

Dear All, In the 2nd paragraph of the attachment can you please explain to me why we are trying to make ## r(z) = z ## and what does "As r is not the identity..." mean?? and how did the line ## L = 0.5*b + ρe^{θ/2} ## come about? Danke...

Dear all, can you please verify if my derivation of the algebraic formula for the rotation isometry is correct. The handwritten file is attached. The derivation from the book (Alan F beardon, Algebra and Geometry) which is succinct but rather unclear is given below. Assume that f (z) = az + b...

/* Last year, in first year I had problems with understanding the Coriolis Force. I asked the lecturer about it and he found a simpler way of explaining it. I thought I had understood. However, I've spent many hours this weekend trying to understand it and it keeps eluding me. That explanation...

Homework Statement Homework Equations Static equilibrium: Net force & net torque = 0 The Attempt at a Solution Am i doing this correctly for part a? [/B]

Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...

An example being its use in the beginning of this document: http://isites.harvard.edu/fs/docs/icb.topic1288789.files/Rotations-Lorentz-Transformations.pdf I haven't read the whole document yet so forgive me if it explains what it means later on.

Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...

Hi, I posted my question on another forum: http://physics.stackexchange.com/questions/143377/one-disk-ring-in-double-rotation-and-sum-of-energy but it is "on hold" and nobody knows where is the error, so I try to post here if you are agree ? I can understand if you close the question...

Find the standard matrix for the rotation of 60◦ about the axis determined by the vector v = (3, 4, 5). do I multiply each x,y,z by pi/3? doesnt seem like it should be that simple

Apart from the the gravitational pull of the Moon and the Sun on the Earth, does the rotation of moon contribute to the tides?

Homework Statement A uniform disk 0.3m in diameter and having a mass of 2 kg isfree to rotate about its horizontal axis on frictionless bearings.An object with a mass of 0.05 kg is attached to a string wound around the rim of the disk. The object is released from rest and descends with constant...

Torque causes a system to rotate about its axis while centripetal force causes a system to rotate about the axis of the separate system that exerted the centripetal force. So does this mean that torque specifically causes rotation and centripetal force causes revolution?

Homework Statement [/B] At t=0, a flywheel has an angular velocity of 3.4 rad/s, an angular acceleration of -0.42 rad/s^2 and a reference line at \theta_0 =0 A: Throigh what maximum angle will the reference line turn in the positive direction B: At what times will the reference line be at...