Angular Definition and 999 Threads

I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I $$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$ n^2 * ħ^2$$ was...

I know that If we have a rigid body rotating clokwise direction,the angular velocity vector should be in the into the screen.But also I know that ##w=dθ/dt## so..Whats the equation that tells us that ##\vec w## is into the screen ? Is it coming from some vector product ? Or we know that...

Homework Statement A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A. Assuming that the pressure and...

Since, under rayleigh's criterion, the angular resolution is dependent on the wavelength of light, wouldn't blue light be more sharply focused by our eyes?

I envision the three fundamental rotation matrices: R (where I use R for Ryz, Rzx, Rxy) I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix. (I understand how I obtain this equation... that is not the issue.) Now I am making the leap to learning about...

Homework Statement There is a man walking on a disk with mass 70 kg and speed 4 m/s. He walks on a circle with radius 1,5 m. How fast does the disk (mass 200 kg and radius 2 m) under him rotates (need to calculate angular velocity)[/B] Homework Equations angular momentum = J * w (J-moment...

Homework Statement Hello! I apologize for my poor setup, first post. I am given a system of two rods, hope you can see my image.http://file:///C:/Users/Mikkel/Downloads/Mek2_exam_Jan2016_final.pdf One along the x-axis with mass = 2m and length = 2l Another perpendicular with the other with...

why don't we feel the difference in Earth's angular velocity between standing on north or south pole versus standing on the equator? Thank you

Homework Statement The function ##f## is defined as follows: \begin{equation*} f(t) = \begin{cases} 1, \text{ when } 2k < t < (2k+1),\\ 0, \text{ when } t = k,\\ 2, \text{ when } (2k-1) < t < 2k, & k \in \mathbb{Z}\\ \end{cases} \end{equation*} What is the period ##T## of the function ##f##...

Homework Statement [/B] A thin, uniform, 3.8kg bar, 80cm long has two 2.5 kg balls glued on at either end. It is supported horizontally by a thin, horizontal, frictionless axle passing through its centers and perpendicular to the bar. Suddenly the right hand ball becomes detached and falls off...

Homework Statement A 2.9-kg particle P is located at [(r)\vec] = 3.3 m [^(x)] + 1.8 m [^(y)] from the origin of the x-y coordinate system shown in the Figure. It moves with a velocity of [(v)\vec] = −4.1 m/s [^(x)] + 2.6 m/s [^(y)]. A force, [(F)\vec] = 2.7 N [^(x)] + 1.4 N [^(y)] acts on the...

Is there a difference between orbital speed and angular speed when an object or star is considered to be in a circular motion around another?

Homework Statement A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ωo, meets a rough inclined plane of inclination θ=60°. The sphere starts pure rolling up the plane with an angular velocity ω. Find the value of ω. Homework...

Hello. Let's have two electrons with same orbital quantum number li and these electrons are in antiparallel; one electron has magnetic quantum number mi = a and and other electron has mi = -a (but we don't know which one has ml = a as we're in coupled representation to talk about total angular...

I can see how it would be conserved for the situation of a star turning into a white dwarf since the object is just contracting. Just like the classic ice skater example. But what about a super nova? Say a star with spin up goes supernova and that the remaining black hole also has spin up but...

Homework Statement We consider a pendulum of length L hanging along the z-axis with a mass (taken to be unity) at the end, attached to an arm of length R free to rotate about the z-axis but restricted to the xy-plane. The system is completely described by the angle of the pendulum rod with...

To radiate energy, the Poynting vector must not drop faster than with the inverse square of the distance. Under what circumstances can EM angular momentum be emitted to the vacuum of space (i.e. without being recovered via inductive coupling) and yet not lead to energy losses through radiation...

Homework Statement A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ]. (i) Explain why we can interpret this as a particle moving...

Homework Statement Homework Equations I= sum m r2 L= r p or L=I W The Attempt at a Solution I= m1 r12 + m2 r22 I= 5.20 (0.9)2+ 2.20(0.9)2= 5.994 kg.m2 Then I used the second equation of second momentum L(Angular momentum) = I W L= 5.994 x 4.60 In the solutions sheet, he used the first...

Homework Statement (This is a problem I myself created, so it may sound a bit trivial/stupid.) A particle of mass m in the xy plane has velocity v and a radius vector r with respect to some origin. After some time Δt, the same particle has velocity v and a radius vector r' with respect to the...

Homework Statement A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds? t=3 seconds wi= 65.0 rad/s α =...

I wonder what would the angular momentum vector look like for these gears. As it rotates, there is no clear direction on where the angular momentum vector is pointing. This object is symmetric. Here's the video about these.

Homework Statement A record player rotates normally at a rate of 18 rev/m. It takes 70 seconds for it to slow down to a stop when you turn it off. Homework Equations Calculate the magnitude of its angular acceleration. The Attempt at a Solution answer key says the correct answer should be...

Homework Statement A 4 g bullet traveling at 500 m/s strikes a disk of mass 1 kg and radius 10 cm that is free to rotate around an axis passing through its center. The bullet’s incoming path is 5 cm above the rotation axis and the bullet comes to rest in the position shown in the figure. At how...

For Q11(b), what is the relation between the angular acceleration ##\alpha## of the bottom right cylinder and its horizontal acceleration ##a_x##? I get ##\alpha=\frac{a_x}{\sqrt{3}R}##, which is half the given answer (7.84) below. After the bottom right cylinder rolls around the top cylinder...

So a light particle is orbiting a massive particle by gravity. We take both particles as spot particles. The light particle makes an eccentric orbit where maximum radius of the orbit equals 2 and minimum radius equals 1. I suppose the mass of the massive particle such that the speed of the...

Homework Statement To lower himself from a balcony an 80kg stuntman grabs a rope connected to a 400kg cylinder with a 1.2m diameter that is free to rotate about its axis of symmetry. What is the stuntman's acceleration as he falls? Homework Equations I missed this on a homework assignment. I...

Homework Statement Two masses have same mass m, both of them are tied by a string and put in a hollow cylinder. When the cylinder start to rotate until the angular speed is ω. The tension in the string is T and the string breaks, both masses move away from the axis in the hollow cylinder...

Homework Statement Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1. Homework Equations Y_1,1 =...

Homework Statement The motion of a particle moving in a circle in the x-y plane is described by the equations: r(t)=3.15, Θ(t)=8.86t Where Θ is the polar angle measured counter-clockwise from the + x-axis in radians, and r is the distance from the origin in m. 1. Calculate the x-coordinate...

Homework Statement Imagine that you are standing on the edge of a cliff looking out over the vista… a sudden gust of wind nudges you off balance and you start tilting out over the edge of the cliff…. Yikes! You start wind milling your arms to regain your balance. A) do you rotate your arms...

Homework Statement "The flywheel rotates with angular velocity of w=0.005theta^2 rad/s. Determine the angular acceleration after it has rotated 20 revolutions. Homework Equations I thought the equations were all but self-evident using the problem description! (See below.) alpha=dw/dt The...

Homework Statement At first I needed to calculate the angular resolution of a telescope (diameter 1m, for visible light) so I used θ=1.22λ/D and got 4.88x10^-7 rad. Now I am asked: "If we wished to use this telescope to image the moon, what is the closest distance two objects can be to be...

Homework Statement Homework Equations Kinematic theorems: The Attempt at a Solution Ok, I'm trying to use another angle, phi, and find some relation betwen phi and theta so I can derive the equation for the angular velocity of rod B with respect to S, but I'm stuck at that point. How...

Consider a flat 2D rigid body rotating about an axis perpendicular to the body passing through a point P that is (1) in the same plane as the body and (2) different from the body's center of mass (CM). In this case does Theorem 7.1 (eqn 7.9) still apply? In the last step of the derivation of...

Homework Statement Two ice skaters of mass ##m = 50\,\mathrm{kg}## each are moving towards each other frictionless on parallel paths with a distance of ##3\,\mathrm{m}##. They both have a velocity of ##v_o=10\,\frac{\mathrm m}{\mathrm s}##. Skater 1 is holding a massless rod of length...

Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...

Hi I have seen an example of commutator of the Parity operator of the x-coordinate , Px and angular momentum in the z-direction Lz calculated as [ Px , Lz ] ψ(x , y) = -2Lz ψ (-x , y) I have tried to calculate the commutator without operating on a wavefunction and just by expanding...

So Imagine a ball moving off a frictionless cliff with a velocity v to the right, at the bottom of the cliff the surface has friction. So after the collision, the x component of the velocity would be reduced, and the angular momentum would be fixed clockwise because the frictional impulse...

Homework Statement Given this diagram, the problem is to find an expression for β/ΘE in terms of X/ΘE and Y/ΘE. Homework Equations β = Θ – α(Θ) Dsβ = DsΘ – Dlsα'(Θ) The Attempt at a Solution I really only need help starting this problem. In my textbook and every document I can find online...

Homework Statement Let ##\left|\psi\right\rangle## be a non-degenerate stationary state, i.e. an eigenstate of the Hamiltonian. Suppose the system exhibits symmetry for time inversion, but not necessarily for rotations. Show that the expectation value for the angular momentum operator is zero...

Homework Statement You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...

Homework Statement At a fair, Hank and Finn play with a horizontal 5.4 m long bar able to rotate about a pole going through its exact center. Hank pushes with 32 N at one end of the bar and Finn pushes with 18 N in the opposite direction at the other end. (Assume both forces are always...

Hi! I don't know if I'm in the right forum of this site but I'm trying anyway. I was just wondering if someone could explain how the step- and impulse response is related to an angular position (of e.g. a spacecraft )? Just a little about the theory since I am trying to actually understand...

Some observed neutron stars rotate hundreds of times per second. Speeds at the surface of these stars are as much as 15% the speed of light. These huge speeds are generated because angular momentum is conserved when a large rotating pre-super nova star collapses into a neutron star. The...

Homework Statement A uniform thin rod of Length L and mass M is pivoted at one end is held horizontally and then released from rest. Assuming the pivot to be frictionless, find a) Angular velocity of the rod when it reaches its vertical position b) The force exerted by the pivot at this time...

Homework Statement I was in lab and we used a mass hanger and disk and plate attached to pulley to and a motion sensor to measure moment of inertia. Angular acceleration was recorded along with other values such as linear velocity and position and all that. The question is: the hanging mass...

My textbook says that for a central force at the origin, the angular momentum is constant, because the derivative rxF is zero since F points radially outwards so it is in the same direction as r. Ok, but what about the angular momentum about a point other than the origin, or the angular momentum...

Homework Statement Assume no friction for 1 - 6 1. Draw a free body diagram of the fly wheel (from above), and a free body diagram of the weight (from side). 2. What force appears in both diagrams? 3. What is the relationship between the torque on the flywheel and the tension in the string...

Homework Statement Homework Equations v=rω conservation of energy The Attempt at a Solution I don't know whether it is correct or not, and I am quite confused in part b it asks the angular speed of the pulley can I say that v=rω since the pulley and box A,B have a common velocity? so is ω...