Problem set 13
... 1. h12i Consider force free motion of a symmetric top with I1 = I2 , as discussed in the lecture. Suppose the axis of the top makes an angle θ , 0 with the fixed direction of L. (a) h6i Find the angle α between the angular velocity vector Ω and angular momentum vector L (α is half the opening angle ...
... 1. h12i Consider force free motion of a symmetric top with I1 = I2 , as discussed in the lecture. Suppose the axis of the top makes an angle θ , 0 with the fixed direction of L. (a) h6i Find the angle α between the angular velocity vector Ω and angular momentum vector L (α is half the opening angle ...
Chapter 13 - AJRomanello
... Mass and Velocity. ρ = mv Angular Momentum (l) – the product of Rotational Inertia and Angular Velocity. L = r x ρ = m(r x v) L = Iω ...
... Mass and Velocity. ρ = mv Angular Momentum (l) – the product of Rotational Inertia and Angular Velocity. L = r x ρ = m(r x v) L = Iω ...
ppt
... Split our rigid body into chunks of matter, we look at each chunk as a simple particle Rigid constraint: distances between particles have to stay constant Thus position of a particle is a rotation + translation from “object space” into “world space” We want to figure out what’s happening wit ...
... Split our rigid body into chunks of matter, we look at each chunk as a simple particle Rigid constraint: distances between particles have to stay constant Thus position of a particle is a rotation + translation from “object space” into “world space” We want to figure out what’s happening wit ...
Document
... This describes the angular momentum of a single particle , where r and v are perpendicular. This would describe a particle moving in a circle. ...
... This describes the angular momentum of a single particle , where r and v are perpendicular. This would describe a particle moving in a circle. ...
The Two-Body problem
... Let us summarize the main spirit of the above analysis. We started with 6 degrees of freedom (r1 , r2 ). Considering motion relative to the CoM reduced this to 3 degrees of freedom, (r). Isotropy of space reduced this to 2 degrees of freedom, (r, ϕ), and then to one, (r). Then, the problem with 1 de ...
... Let us summarize the main spirit of the above analysis. We started with 6 degrees of freedom (r1 , r2 ). Considering motion relative to the CoM reduced this to 3 degrees of freedom, (r). Isotropy of space reduced this to 2 degrees of freedom, (r, ϕ), and then to one, (r). Then, the problem with 1 de ...
Statics 210 Chapters 2.1 – 2.3
... Angular Momentum • “Moment” of the particle’s linear momentum about Point O. • Scalar Formulation – If the particle is moving along a curve lying in the x-y plane. ...
... Angular Momentum • “Moment” of the particle’s linear momentum about Point O. • Scalar Formulation – If the particle is moving along a curve lying in the x-y plane. ...
Angular Momentum - Houghton College
... IV. Torque (rotational force): = rFsin V. Angular Momentum: A. ...
... IV. Torque (rotational force): = rFsin V. Angular Momentum: A. ...
A moving object has a tendency to keep moving, this is momentum
... will speed up. Neutron stars are formed by the collapse of a star's matter following a supernova. ...
... will speed up. Neutron stars are formed by the collapse of a star's matter following a supernova. ...
Relativistic angular momentum
""Angular momentum tensor"" redirects to here.In physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics.Angular momentum is a dynamical quantity derived from position and momentum, and is important; angular momentum is a measure of an object's ""amount of rotational motion"" and resistance to stop rotating. Also, in the same way momentum conservation corresponds to translational symmetry, angular momentum conservation corresponds to rotational symmetry – the connection between symmetries and conservation laws is made by Noether's theorem. While these concepts were originally discovered in classical mechanics – they are also true and significant in special and general relativity. In terms of abstract algebra; the invariance of angular momentum, four-momentum, and other symmetries in spacetime, are described by the Poincaré group and Lorentz group.Physical quantities which remain separate in classical physics are naturally combined in SR and GR by enforcing the postulates of relativity, an appealing characteristic. Most notably; space and time coordinates combine into the four-position, and energy and momentum combine into the four-momentum. These four-vectors depend on the frame of reference used, and change under Lorentz transformations to other inertial frames or accelerated frames.Relativistic angular momentum is less obvious. The classical definition of angular momentum is the cross product of position x with momentum p to obtain a pseudovector x×p, or alternatively as the exterior product to obtain a second order antisymmetric tensor x∧p. What does this combine with, if anything? There is another vector quantity not often discussed – it is the time-varying moment of mass (not the moment of inertia) related to the boost of the centre of mass of the system, and this combines with the classical angular momentum to form an antisymmetric tensor of second order. For rotating mass–energy distributions (such as gyroscopes, planets, stars, and black holes) instead of point-like particles, the angular momentum tensor is expressed in terms of the stress–energy tensor of the rotating object.In special relativity alone, in the rest frame of a spinning object; there is an intrinsic angular momentum analogous to the ""spin"" in quantum mechanics and relativistic quantum mechanics, although for an extended body rather than a point particle. In relativistic quantum mechanics, elementary particles have spin and this is an additional contribution to the orbital angular momentum operator, yielding the total angular momentum tensor operator. In any case, the intrinsic ""spin"" addition to the orbital angular momentum of an object can be expressed in terms of the Pauli–Lubanski pseudovector.