Rotation Definition and 1000 Threads

i read formulae in textbook : [α]λt°C = Θ/L*C ...(i) where Θ is rotation in light and L is length of tube and C is concentration in gm/litre if we consider tube of lenth L and cross section area 'A' then C= M/A*L M is mass of sample so (i) becomes [α]λt°C = Θ/[M/A] so are...

So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...

I'm working on a project that will find the coefficient of drag on bombs with various added drag features by modeling flow over the bomb at various angles of attack using CFD. The problem is that I'm not sure if bombs with fins rotate while they are falling due to gravity, and if so, how I...

A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if : 1- the ramp is frictionless...

Homework Statement Hello! English is not my native language so I hope the terminology is right. Q: Find the volume generated by the curve y=1/x+2, positive x- and y-axis and the line x=1. Calculate the volume obtained by rotation around the: a) x-axis b) y-axis Homework...

Homework Statement A homogeneous cube of sides l is initially at rest in unstable equilibrium with one edge in contact with a horizontal plane (θ = 45 degrees initially). The cube is given a small angular displacement and allowed to fall. What is the angular velocity of the cube when one face...

Suppose you have a body floating in a rotating superfluid. Maybe a speck of dust. Would it rotate? What if you have two bodies connected in some way. Would this system rotate around its center of mass?

Homework Statement A uniform right circular cone of height h, half angle α, and density ρ rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time \tau. Find expressions for the kinetic energy and the components of...

Torque Free Rotation...again... Hello Forum, I have read an old, but good, thread about torque free rotation: https://www.physicsforums.com/showthread.php?t=405781 I am still unclear on how, from the inertial (lab) frame of reference, the moment of inertia I, which is a tensor with 9...

So I was doing my calc homework when I stumbled upon this thought: lets say you were trying to find the solid of rotation of y=x^2 around the x-axis over the interval [-2,2]. the traditional method would entail pi * integral from -2 to 2 of (x^2)^2 dx while this is easier for a simple...

Assume that the arbitrary-shape object shown has a torque applied at the black X with a circle, and is free to rotate about the X axis. Assume that the object is also constrained by a pin at this torque input point, parallel to the X-axis. The CG of the object is the blue plus sign, and there...

I'm having trouble with two review questions: 1) Julie has been hired to help pain the trim of a building, but she is not convinced of the safety of the apparatus. A 5 m plank is suspended horizontally from the top of the building by ropes attached at each end. Julie knows from previous...

Homework Statement This is not a HW problem, but something I am trying to prove/disprove for my own knowledge. I have a tube pinned at both ends and inclined in the x-y plane. The pin locations can both move freely in space but subject to the constraint that the tube will not stretch or...

Homework Statement PS:The compound gear to the right is located inside a truck, whose engine rotates the driving gear with torque of 816 N*m. Assume that in the figure to the right, each of the smaller gears have a radius of 5.0 cm, and the larger gears have a radius of 25cm. Also, assume...

Homework Statement A homogene rod with length "l" is placed vertically, and a nail is stabbed on the top of the rod (now the rod has an axis). And then an impulse is given on the rod with the separation between the impulse given to the rod's axis is "d". Earth gravitational acc is represented...

A homogene rod with length "l" is placed vertically, and a nail is stabbed on the top of the rod (now the rod has an axis). And then an impulse is given on the rod with the separation between the impulse given to the rod's axis is "d". Earth gravitational acc is represented as g, the mass of the...

Homework Statement Given below are three geometrically defined linear transformations from R3 to R3. You are asked to find the standard matrices of these linear transformations, and to find the images of some points or sets of points. a) T1 reflects through the yz-plane b) T2 projects...

Homework Statement A 75g mass sits 75cm from the center of a rotating platform undergoing a uniform angular acceleration of 0.125rad/s . The coefficient of static friction between the mass and the platform is 0.250. What is the speed of the mass when is slides off? A. 0.889 m/s B. 1.26...

I don't really understand the explanation given in Binney's text about: Hamiltonian is given by: H = \frac{\hbar^2}{2} \left( \frac{J_x^2}{I_x} + \frac{J_y^2}{I_y} + \frac{J_z^2}{I_z} \right) Orient axes such that ##I_x = I_y = I##. H = \frac{\hbar^2}{2} \left( \frac{J^2}{I} +...

Homework Statement Calculating solar of the sun through observing sunspots. We are given a series of photos of the sun over a period of time where we can see sun spots. I am assuming the way to calculate would be to work out the longitudinal angles of the sun spots in the different photos and...

I'm not sure if this belongs in Astronomy or Astrophysics. Todays APOD featured the rotation of the sun about its own axis. It seems to me that the axis of rotation of the sun should be aligned with the axis of rotation of the plane of rotation of the planets, i.e. the ecliptic, or more...

We have had a number of threads on how to synchronise clocks around a rotating ring. One method of doing this is to start all the clocks on the ring via a signal from the centre of the ring. This method has the advantage of being transitive, but has the disadvantage that the local one-way speed...

Why do celestial bodies follow different laws of physics than terrestrial bodies? A non-rotating object has a point on its axis, or axle, continually aligned with a point on the object. An axis is virtual, or imaginary; an axle is real and we live in a real physical world. In a real physical...

we know that an electron rotates about its own axis.similarly does the electron too rotates about its own axis? and does nucleus and electron vibrate in an atom?

Does the "rotation" of an electron have any meaning? Not sure if this is the right subforum, but thinking of this was rather head-ache inducing. Is there any sensible meaning to claiming that an electron rotates 360 degrees? Intuitively I would initially say yes, but on second thought I would...

Homework Statement The problem is as follows. I have two spins, m_S and m_I. The first spin can either be \uparrow or \downarrow , and the second spin can be -1, 0 or 1. Now, I envision the situation as the first spin being on the bloch sphere, with up up to and down at the bottom. What I...

As known the DNA molecule has got negative electric charge. Imagine that linear (almost like a straight arrow) DNA is placed in water solution and we turn the electric field on. I would like to know if the DNA molecules can orientate/rotate so that they to stay along the field lines of the...

Earth has a huge angular velocity regarding its rotation. Now let's imagine that the Earth has the velocity of 400 km/s relative to some inertial frame. What will be the velocity of Earth when we take the rotation into account combined with inertial motion? How do the 2 combine? Thanks in...

Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...

I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish). I don't understand the second line. How does he separate the matrix in two different parts? Thanks for your time.

I am thinking about how to find the volume rotate around its function.Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volumeThank you CBARKER1

Does a body rotating about an axis also rotate about any other axis? Eg. Cars on a racetrack may be rotating about a vertical axis passing through the centre of the track but can they also be considered to be rotating about a vertical axis passing through the spectators' stand?

I know very little about mechanical systems, but what kind of small simple gear system can do this; I have a motor, it turns one way, I guess it would turn a spiral bevel, but it only goes into one direction since the motor turns continuously in one direction, what mechanical solution allows...

Homework Statement Obtain the surface area when the curve y=ex, 0≤x≤1, is rotated about the x-axis Homework Equations Surface Area = 2∏a∫b x√(1+(dy/dx)2)dx The Attempt at a Solution I started with the the equation, Surface Area = 2∏0∫1 x√(1+e2x)dx. However, whichever way I try to...

Using http://www.mymathforum.com/download/file.php?id=6171 and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix} r'\\ z'\\ \end{bmatrix} = \begin{bmatrix} cos(\phi) & sin(\phi)\\ -sin(\phi) & cos(\phi)\\ \end{bmatrix} \begin{bmatrix} r\\ z\\ \end{bmatrix} and...

Homework Statement The Singapore Flyer is te world's largest Ferris wheel. It's diameter is 150m and it rotates once every 30 min. a) Find the Magnitude of the average velocity b) Find the average acceleration at the wheel's rim. The Attempt at a Solution a) |v→| = Δs/Δt=75m.2π/30mins =...

Hi everyone, here's the situation: Everyone knows that you can simulate artificial gravity by rotating a space ship. Usually these scenarios include an atmosphere with regular air inside. I know that the inclusion of air has an influence on the effects inside by way of friction. How different...

Hello! Talking about propagation of an electro-magnetic field in a non-isotropic medium, I've got some troubles with the expression in object, used to show the Faraday rotation of the polarization of a field. Homework Statement An electro-magnetic field enters a particular medium...

Consider two cartesian coordinate system xyz and x` y` z` that initally concide. The x` y` z` undergoes three successive counterclockwise 45 rotations about the following axes: first, about the fixed z-axis;second, about its own x`-axis( which has been now rotated); finally, about its own...

Homework Statement Suppose an E-field is rotated by angle ø2. Express ø2 in terms of: Homework Equations The Attempt at a Solution I used the rotation matrix, and compared LHS and RHS but it led to nowhere: E'= RE \left ( \begin{array}{cc} E_1' sin (ky-ωt+ø_2) \\ 0 \\ E_2' cos...

Homework Statement Hi, I am not sure if this is the right place for my question but here goes! The stress tensor in the Si coordinate system is given below: σ’ij = {{-500, 0, 30}, {0, -400, 0}, {30, 0, 200}} MPa Calculate the stress tensor in the L coordinate system if: cos-1a33=45°, and...

Homework Statement This is more of a conceptual doubt. Why does the axis being called as the axis of rotation of a rolling body have to be at rest with respect to some frame of reference? What is the definition of axis of rotation? When is an axis called an axis of rotation?

Hi all, Suppose we go in space where no gravity and friction exists. If there is a bar, in say - horizontal plane and we apply a force at one end of the bar, in this plane and perpendicular to the bar. Will that bar rotate and translate or it will only undergo pure translational motion...

In another thread WannabeNewton mentioned: and gave this reference: Until WBN mentioned it, I had never given any thought to the difference between these methods of measuring rotation, so I would like to explore those ideas further here, particularly in relation to the Kerr metric. Consider...

I was wondering if a galaxy could be perfectly orbiting to create a sort of axis of rotation, with a period being like 50 million years, or is it impossible because of some property that elliptical galaxies have? If it is possible, what is the probability that it exists in our observable...

Hi there, I am confused. I want to work out the acceleration that a body placed on a wheel of radius 10 mm going at a frequency of 3Hz would experience in the x y and z axis. The equations for rotation don't make this clear. They just give me one basic equation for acceleration Can you...

Homework Statement A merry-go-round is sitting in a playground. It is free to rotate, but is currently stationary. You can model it as a uniform disk of mass 220 kg and radius 100 cm (consider the metal poles to have a negligible mass compared to the merry-go-round). The poles near the edge...

It is well known 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 appointed that...

Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...

The problem asks to find the standard matrix for the composition of these two linear operations on R2. - A reflection about the line y=x, followed by a rotation counterclockwise of 60o. This is how I proceeded. y=x $\begin{bmatrix}0&1\\1&0 \end{bmatrix}$ counter clockwise 60degs...