Angular Definition and 999 Threads

I'm trying to deduce the angular momentum ( for a rigid body ) on my own, and here is the problem I face. By introducing the angular momentum of a tiny piece in rigid body (" i ") as : Li = ri × pi Li = ri × mi vi --------------------------------- [ Line 1 ] Li = ri × mi ri ωi To find the...

I' m trying to derive the work done by a torque from W = ∫ F ⋅ ds and I' ve looked up the internet, it said: W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 ) it can be written as W = ∫ F ⋅ dθ x r this is a vector triple product , thus can also...

I've started on "Noether's Theorem" by Neuenschwander. This is page 35 of the 2011 edition. We have the Lagrangian for a central force: ##L = \frac12 m(\dot{r}^2 + r^2 \dot{\theta}^2 + r \dot{\phi}^2 \sin^2 \theta) - U(r)## Which gives the canonical momenta: ##p_{\theta} = mr^2...

Hello 1. Homework Statement The dipole moment of an ammonia molecule is ##d_0=5*10^{-30} C.m##.If we apply a static electric field of ##\mathcal { E }=1*10^{6 }V*m^{-1}## to an ammonia molecule initially in the state ## |ψG⟩## where the nitrogen molecule is considered to be on the left,we make...

Hello, I encountered the following statement in my lecture notes and there is a couple of things I don't understand:"Let's consider two particles with spins ##s_1 = \frac{1}{2}## and ## s_2 = 1## with a spherically symmetric interaction potential. Assume these two particles are in a two...

Homework Statement Not a HW problem, but a "me re-thinking things" problem. Please tell me where my thinking is flawed: You have an ice skater with no net external torques acting on him/her. (We are analyzing the time after they have to get an external torque on them by pushing off of the...

Homework Statement A uniform thin rod AB is equipped at both ends with the hooks as shown in the figure and is supported by a frictionless horizontal table. Initially the rod is hooked at A to a fixed pin C about which it rotates with a constant angular velocity w1 . Suddenly end B of the rod...

Homework Statement "A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD...

Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...

Homework Statement A particle (5 kg) moves with constant velocity 2 m/s along the straight line 2y=3x+4, the angular momentum of the particle about origin is? Homework Equations L=r x p The Attempt at a Solution For a 2d problem we take the component of velocity perpendicular to the point...

I have a question, let’s say I’m holding a long piece of wood such as. 1’ x 6’ plank and I’m rotating it in a circle by spinning around with my hands extended, I suddenly let go, what happens to the velocity of the wood since every point on the wood that is a different distance from the center...

Homework Statement A plank of wood sits on top of two rollers with radius of 44.4 cm. The plank is pulled forward so it moves at a constant acceleration of 2.24 m/s^2, starting from rest, and the rollers roll without slipping along the ground and in contact with the plank. What is the...

I have a disc that is rotating due to air being blown at its outer radius. The incoming relative velocity of the air is high, therefore the effect of friction supersedes the effect of conservation of angular momentum. The tangential portion of this velocity decreases due to the friction as it...

Homework Statement A disk of radius ##r## and mass ##m## rolls down an inclined plan. It reaches the end of the plane with velocity ##v_{f}## and collides with a vertical rod of length ##L## and mass ##M## sticking with it. See figure. What is the angular momentum magnitude and direction...

If talking about a particle rotating around an axis away from it by r. if the particle is moving with constant angular velocity ω. is the linear velocity constant or no? Now what I know is that since we have Vt= ωr, so r doesn't change, as well as ω, so Vt is said to be constant. but I think...

Homework Statement A ball of mass ##m## is attached to a massless string of length ##L##. The ball is released from rest as shown in the figure and as it reaches the bottom of the circle, the string wraps around a nail which is a distance ##d## below the center of the circle. What is the...

1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...

Homework Statement A 2.4 kg particle-like object moves in a plane with velocity components vx = 25 m/s and vy = 80 m/s as it passes through the point with (x, y)coordinates of (3.0, −4.0) m. (Express your answers in vector form.) (a) What is its angular momentum relative to the origin at this...

If ##\theta## is angular displacement, does ##\frac{d^2\theta}{dt^2} = (\frac{d\theta}{dt})^2##? Proof?

Homework Statement A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I Homework...

Homework Statement AB is a rod of length 10 m that is leaning against the wall. Given variables are shown in the diagram. Find angular velocity of A wrt B. https://imgur.com/a/8bEdYhN I have a doubt in one step that I will highlight in "The attempt at a solution" part. Homework Equations...

For illustration purposes, I have attached an image of the line with the angle that I want to calculate. I am trying to determine the angle of rotation and the calculation that I am using currently is as below: angle = math.atan2(y,x) I use this formula to calculate the rotation for A and A'...

According to the book "transport phenomena" by Lightfoot, Byron and Stewart if you take the cross product of the equation of motion (for very small element of fluid) and the position vector ##r## you get the equation of change of angular momentum. After some manipulation of vectors and tensors...

Homework Statement I'd like to show, if possible, that rotational invariance about some axis implies that angular momentum about that axis is conserved without using the Lagrangian formalism or Noether's theorem. The only proofs I have been able to find use a Lagrangian approach and I'm...

Homework Statement A disk [m=0.1 Kg; R=0.1 m] rotates about its center of mass [w=40 rad/s], on a smooth floor. A bar [m=0.1 Kg; lenght=R=0.1 m] moves on the floor with a speed Vb=4 m/s. At one point, the bar hits disk's edge in an inelastic collision, and they start rotating together. A)[Fixed...

Homework Statement A pendulum with a light rod of length ##l## with a bob of mass ##m## is released from rest at an angle ##\theta_0## to the downward vertical. Find its angular velocity as a function of θ, and the period of small oscillations about the position of stable equilibrium. Write...

Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring...

My intuition is if an object is orbiting a centre, it is accelerating as the direction of its vector constantly changes, i.e a ball orbiting a stick because they are tied by a string. I don't understand why Earth's spin does not slow down, if we think of Earth as lots of individual atoms, those...

We have an automotive swivel seat that turns from the initial seating position to the final position outside the vehicle (90 degree swivel in 15 seconds). We would like to calculate the torque required for rotating the seat along with the person. We have calculated the inertia of the movable...

Hey all, so I’ve been learning nonlinear acoustics and have encountered a conceptual hurdle in my studies. When using a model, such as a form of the classical Burgers equation, to propagate sound waves, you generally have a “characteristic angular frequency” in the equation (often represented by...

Homework Statement Consider two pairs of operators Xα, Pα, with α=1,2, that satisfy the commutation relationships [Xα,Pβ]=ihδαβ,[Xα,Xβ]=0,[Pα,Pβ]=0. These are two copies of the canonical algebra of the phase space. a) Define the operators $$a_\alpha =...

I have seen so many questions and confusion about the difference between angular velocity/speed and angular frequency. Usually, answers were always given in the context of uniform circular motion (angular speed) and simple harmonic oscillation (angular frequency), but this is what causes the...

Homework Statement A particle is moving parallel to x-axis in the positive direction with velocity v such that at all the instants the y -axis component of its position vector is constant and is equal to 'b'. Find angular velocity about origin. Homework EquationsThe Attempt at a Solution I...

Homework Statement A certain odd-parity shell-model state can hold up to a maximum of 4 nucleons. What are its values of J and L? What about an odd-parity shell-model state with a maximum of 6 nucleons? Homework Equations Parity = (-1)L J = L+S Total angular momentum, J, is equal to orbital...

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Homework Statement A rod (mass M, length L) is placed vertically on a smooth horizontal surface. Rod is released and after some time velocity of COM is v downwards and at this moment rod makes 60 degrees with horizontal. Find angular momentum of rod about Instantaneous center of rotation...

Homework Statement A circular ring (2m, R) with a small insect of mass m on its periphery, is placed upon smooth horizontal surface (axis of rotation passing through center and perpendicular to the ground i.e disk is lying horizontally) . The insect starts moving with velocity v w.r.t ground...

Homework Statement two discs of radii r and 2r are pressed against each other. Initially disc with radius r is rotating with angular velocity w and other disc was stationary. Both discs are hinged at their respective centers and free to rotate about them Moment of inertia of 1st disc is I and...

Homework Statement suppose you're sitting on a rotating stool holding a 2kg mass in each outstretched hand, if you suddenly drop the masses, will your angular velocity increase, decrease or remain the same? Homework Equations dL/dt=net torque when net torque is 0, L=constant=Iw therefore...

Homework Statement Assertion- If linear momentum of particle is constant, then its angular momentum about any axis will also remain constant Reason-Linear momentum remains constant when net force is 0, angular momentum remains constant when net torque is zero which of these statements is/are...

Homework Statement A uniform rod (M, L) is rotated about a point L/3 from its left end. Angular momentum about O Homework Equations 1) L=I(cm)w for purely rotating body 2) L(orbital)= M*v(cm)*perpendicular distance(r) 3) L(spin)= I*w The Attempt at a Solution I got the correct answer in two...

Homework Statement A disk is undergoing pure rolling motion with speed v. The radius of the disk being R and mass M. Then the angular momentum of the disk about the 1)bottom most and 2)top most point Homework Equations 1) L(orbital) = m*v*r where v is the velocity of cm which is...

Homework Statement A 7.3-cm-diameter baseball has mass of 150 g and is spinning at 230 rad/s . Treating the baseball as a uniform solid sphere, what is its angular momentum? I'm about to pull my hair out because I feel like I understand everything about this problem perfectly and yet I'm still...

Homework Statement Homework Equations $$\mathcal{L}=T-U$$ $$\omega= \frac{d\phi}{dt}$$ $$I=mr^{2}$$ The Attempt at a Solution My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following: $$K.E...

Homework Statement Four particles of mass 1 Kg each, are moving on a plane with the velocities given in the figure. Homework EquationsThe Attempt at a Solution First I calculated the position of the CoM: Xcm=7/4(i + j) Then I calculated the velocity of the CoM: Vcm= ½i + ¼j For the internal...

The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, *Astrophysics in a Nutshell by Dan Maoz pp.220-221*, I am having some trouble trying to understand the notion of **angular diameter...

Hello, in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...

From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following: h = wr^2 = ab * n How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or...

Homework Statement 4 persons each with mass m stand out on the edge of the carousel that rotates with angular velocity W0. carousel has mass 4m, radius r and inertia I = 2mr^2. The 4 persons then go all the way to the center of the carousel. Show that the final angular velocity W1 = 3W0 See...