Rotation Definition and 1000 Threads

I need someone with more experience in the field who has knowledge of excel to check over my work. Given the gravitational attraction between two bodies is F = (GMm)/r^2, and the centripetal force required to keep a body in orbit is F = (mv^2)/r, therefore (mv^2)/r = (GMm)/r^2 therefore...

Homework Statement Two 8.0N forces act at each end of a beam of length 0.60m. The forces are parallel and act in opposite directions. The angle between the forces and the beam are 60 degrees. What is the torque of the couple exerted on the beam? 1. 2.4Nm 2. 4.2Nm 3. 4.8Nm 4. 9.6Nm Homework...

For the distance function ##(\Delta s)^2 = (\Delta r)^2 + (r \Delta \theta)^2##, the rotation matrix is ##R(\theta) = \begin{pmatrix} cos\ \theta & - sin\ \theta \\ sin\ \theta & cos\ \theta \end{pmatrix}##. That means that for the distance function ##(\Delta s)^2 = (\Delta r)^2 +...

The direction of the torques in the following working will be found using: \vec{\tau} = \vec{r} \times \vec{F}. When viewed from above, the counterclockwise rotation of the blades produces a torque out of the page: As the angular momentum (right-hand corkscrew rule) is also out of the page...

Hello, I'm trying to figure out what effect does the rotation point where you choose to hold a drumstick have on the rebound of the stroke. Drummers usually find this point by feel, or by fiding out at which rotation point the stick produces the most rebounds. I'm curious to know what are the...

Homework Statement Derive the infinitesimal rotation operator around the z-axis. Homework Equations My book gives this equation (which I follow) with epsilon the infinitesimal rotation angle: $$ \hat{R}(\epsilon) \psi(r,\theta, \phi) = \psi(r,\theta, \phi - \epsilon) $$ but I just don't get...

Hi, just curious: I was able to simulate rotation motion in Alice software , as a combination of two motions: 1)Moving forward 2)Turning left (I can choose the rate at which each of these happens , in terms of meters and revolutions respectively.) Done simultaneously, at just the right rate...

HI - we know that the orbit of mercury precesses (I hope I am using the right terminology here). Which basically means that the orbit seems to undergo some sort of rotation in the ecliptic plane. Does this also mean that the period of Mercury's orbit as seen from the Earth is not uniform but...

How much affect does the rotation of the Earth (such as drag friction) have on the motion of the atmosphere (if any). Respectfully, Hagar

question - Consider the cobination of two discs(attached) , then what will be the velocity of falling disc centre as a function of h. Both discs are identical and string doesn't slip relative to disc. Relevant equations - Conservation of energy . Torque=r×F Force=ma An attempt to the question...

Hi all, I have a small DC motor which turns at 20 rpm. The shaft diameter is 6mm, giving a circumference of 18.85 mm. What I want to do is get an effective rate of 30 rpm. Can I do this by simply attaching a spool or spindle to the motor output shaft with a larger diameter? If so, would it...

Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM. What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation? If not, are the 3...

Homework Statement the sun collapses to the size of the Earth (approximately 1/100 the original diameter), The current average rotation of the sun is approximately 30 days. Homework Equations what would be the new rotational period (time to spin once)? The Attempt at a Solution I know that in...

I was reading a section in my book discussing the commutativity of infinitesimal and finite rotations. In the book the authors try to set up a scenario to explain why finite rotations are not commutative. The following is an excerpt from the book regarding this language: "The impossibility of...

Suppose a position vector v is rotated anticlockwise at an angle ##\theta## about an arbitrary axis pointing in the direction of a position vector p, what is the rotation matrix R such that Rv gives the position vector after the rotation? Suppose p = ##\begin{pmatrix}1\\1\\1\end{pmatrix}## and...

Ok, I solved the question posed in the attached image. I did so by using the car's center of mass as the location of my axis of rotation, generated torque and force equilibrium equations, and solved for all unknowns. When I try to use another location for my axis of rotation, e.g., the point...

Can anyone explain to me why the following operators are rotation operators: \begin{align*}R_x(\theta) &= e^{-i\theta X/2}=\cos(\frac{\theta}{2})I-i\sin(\frac{\theta}{2})X= \left(\!\begin{array}{cc}\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\ -i\sin(\frac{\theta}{2})&...

Homework Statement We consider Rectangle Parallelepiped on a board and a=1m ; b=2m and c=3m. The face a and b is considered touching the board. there’s no sliding; we tilt the board so a is horizontal. Q: Starting from which angle we can see a rotation? Homework Equations I want to know how...

Homework Statement Prove that ## e^{2\pi i \mathbf{n\cdot J}/\hbar} |j,m\rangle = (-1)^{2j}|j,m\rangle ##. This equation is from Ballentine's QM book. The term in front of the ket state in the LHS is a rotation operator through ##2\pi## angle about an arbitrary direction ##\mathbf{n}##...

Suppose for a moment you had a circular copper disc placed concentrically in the air gap between the poles of an upper and a lower circular magnet, the outer faces of the upper lower magnet being connected by a pole piece so as to complete the magnetic circuit. The edge of the copper disc is...

Homework Statement Let's suppose we have a [cuboid](http://en.wikipedia.org/wiki/Cuboid) of dimensions ##a \times b \times c##. We put it on an inclined plane of an angle ##\alpha## so that only one edge of length ##c ## touches the plane. In time ##t = 0 ## the cuboid doesn't rotate. Let the...

Homework Statement Imagine this: A rod is attached at one end to a rotating shaft. So, as the shaft rotates from 0 to 90 degrees back-and-forth (in the xy plane), so does the rod. My goal is to measure the instantaneous acceleration of the rod while its moving. I have a few 3-axis...

if we fly over a moving train at the speed of train can we out run it?? it not, how come we fly at 255m/s when Earth is rotating at 460m/s and we reach from paris to america

Homework Statement A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions. The separation between the wheels is L. The friction coefficient between each wheel and the plate is N. Find the time period of oscillation of the plate if it is...

Homework Statement The problem is this: A car is evenly slowing down from 30 km/h to 0 in the time of 2 seconds. Radius of its wheels is 30 cm. What is its angular acceleration and what total angle will the wheel describe until it stops? How many turns does the wheel make and what is the length...

Hello, So my issue is as follows: You have a car going at a constant speed and the right side of the car hits a ramp which causes that side to elevate and cause the car to rotate about its x axis. What I need to figure out is how fast does the car need to hit the ramp to cause a rollover...

Hey folks, I created and verified a model with hand calculations, and decided to re-use my same logic.. Which now is giving me false numbers. Was wondering if you guys could help me out. Setup/Verification (See attached Reaction_Forces picture): Body in motion being held down by straps...

Will the Earth's rotation someday be synchronized with its revolution around the Sun (one rotation on the axis per revolution), such as the Moon around the Earth? If not, why?

Homework Statement Consider the set of operations in the plane that includes rotations by an angle about the origin and reflections about an axis through the origin. Find a matrix representation in terms of 2x2 matrices of the group of transformations (rotations plus reflections) that leaves...

Homework Statement What is the closest celestial object that has bound synchronous rotation with another object? Homework Equations - The Attempt at a Solution I am almost sure it's Moon.

Hey all, I'm stuck on this problem and not sure how to proceed/if I'm in the right direction. Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below (A) find the direction...

I hope this is in the right forum. I'm trying to see how to calculate rotation curves for a spiral galaxy. The data I have is brightness profile (mag/arcsec^2) and observed rotation curve - to see how it fits. from what I found I need the total mass, and for that I need the surface mass density...

Homework Statement An electron is rotating around a proton (at rest) in a perfect circular orbit. If the radius of the orbit is r=10^-10 m, how long is the rotation period [hint: the radial acceleration is entirely due to the electric force] k=9*10^9 q=1.6*10^-19 Homework Equations 1...

I know this is not typical and you aren't suppose to solve the problem for the person just give hints, however my teacher has not taught this and expects us to know it. For whatever I cannot grasp how to do this any help would be great thank you! 1. Homework Statement The turntable of a...

Hey Guys, Can you tell me how to solve this one, Need not give me direct answers but just take a look at this : Consider two disks A and B of equal radius, let m1 be the mass of disk A and m2 be the mass of disk B, Both are moving towards each other with Velocity v1 and v2 respectively, If they...

When you put o disc on top of a plank and if you pull the plank, the disc rotates but stays stationary. Here the friction between the plank and disk produces an unbalanced torque and hence it spins.But this friction should also cause an acceleration in the disc right? Then why does it remain...

Greetings all, First time poster and an absolute neophyte, please forgive my utter cluelessness in advance. So I was reading "Why does the Milky Way rotate?" (http://phys.org/news/2015-02-milky-rotate.html), and it brought to mind a question that's niggled at me every so often when my...

I'm looking for sources of data for galactic rotation curves but need not only the observed rotation curves but also the expected (Keplerian) curve data to load into a spreadsheet to experiment with. After extensive searching I found a few pockets of data for observed velocities but not for...

I'm still very early on in my reading, so forgive me if this question isn't coherent. In the "historical introduction" section of the 1920 University of Calcutta translation of the original papers of Einstein and Minkowski available via the MIT online archive, mention is made of the fact that...

How would I go about creating something like a hatch, that could be arrested at any instance. I am looking for a solution for a 0-90, 90-180, and 0-180 degree range. A 360 degree solution such as a whiteboard, would work just as well. If you know how this can be made, or know a link that...

Homework Statement To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of If the centrifuge diameter is 13.5m , what should be its rotation...

Homework Statement Find volume when the area rotates around a line. Homework Equations x=y^2 x=1-y^2 about x = 3 The Attempt at a Solution Could someone please check my formula for Area? I have pi[ (3-(y^2))^2 - (2-(y^2))^2 ] which gives me the integral pi[5y-(2/3)y^3]. I think...

Hi! I'm new here, so I apologize on beforehand for any mistakes I may make (grammar/wrong thread etc.). Currently we are doing a project for our exam in my class, and in my group we chose to focus on the following scenario: On a spinning "plate" (you know, like a merry-go-around... sorry, I'm...

Homework Statement How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines? I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance...

Hello, first post! I'd apreciate some help on finding out the calculus for knowing the motor's torque needed for mantaining 2 vertical disks ø46cm, 30kg each at 300rpm, taking into acount 3 generic bearings friction that hypotetically is 0.5Nm friction torque I'm having some trouble trying to...

I would like to calculate the change in linear position of a point on a bar whose center of mass is changing as the bar rotates. Assume an angular velocity of pi-rad/s, a negligible mass for the bar, and a mass of 1-kg for the weight (which is what is moving and causing the center of mass to...

How do you prove that rotation of a vector is a linear transformation? It's intuitive (although not completely crystal clear to me) that it is a linear transformation at the 2d level, but how do I prove it to myself (that this is a general property of rotations)? For example, rotate vector...

Homework Statement I am trying to answer the following question: Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain...

Hey, let's say that in 2D space we have a 2x2 rotation matrix R. Normally you could multiply this rotation matrix by a 2x1 column matrix / vector X. In that case it would be XR to get the vector rotated in the way described by R. Now what I'm wondering is, what if I had 3 column vectors that I...

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...