Physics 6010, Fall 2010 Symmetries and Conservation Laws
... equations of motion. Indeed for systems with one degree of freedoms, a conservation law usually determines everything! More generally, if there are enough conservation laws it is possible to completely solve for the motion. On the other hand, I cannot emphasize enough the fact that almost all dynami ...
... equations of motion. Indeed for systems with one degree of freedoms, a conservation law usually determines everything! More generally, if there are enough conservation laws it is possible to completely solve for the motion. On the other hand, I cannot emphasize enough the fact that almost all dynami ...
Angular Momentum Solutions
... exerting any torque, so the angular momentum is conserved. On the other hand, the friction force acting on the child is doing work, because she is moving towards the center (which is the direction of that force). Child on a MerryGoRound 02 v1 031 10.0 points A child of mass 52.8 kg sits on the edge ...
... exerting any torque, so the angular momentum is conserved. On the other hand, the friction force acting on the child is doing work, because she is moving towards the center (which is the direction of that force). Child on a MerryGoRound 02 v1 031 10.0 points A child of mass 52.8 kg sits on the edge ...
Problem 1: Kinematics (15 pts) A particle moves along a straight line
... long does the trip take? How far is the boat from the port B after crossing? ...
... long does the trip take? How far is the boat from the port B after crossing? ...
المحاضرة الثالثة Circular Motion
... a- V=squar root(2*R*g) where R :radius of the planet g :the gravitational acceleration at its surface b- A car with a mass 2500kg moving with velocity 2ookm/hr ,a break force applied on it to stop after 5 sec find The acceleration The distance traveled before it stopa ...
... a- V=squar root(2*R*g) where R :radius of the planet g :the gravitational acceleration at its surface b- A car with a mass 2500kg moving with velocity 2ookm/hr ,a break force applied on it to stop after 5 sec find The acceleration The distance traveled before it stopa ...
Stacey Carpenter
... Along the same lines, Ft = mat. What does at become? Remember a = ∆v/t? Rearrange it to form at = ∆v. The units are (m/s2)s. The seconds cancel, leaving m/s, or velocity. So, Ft = m∆v, or Ft = ∆mv. This can also be derived from two equations relating to acceleration. a = F/m and a = ∆v/t. ...
... Along the same lines, Ft = mat. What does at become? Remember a = ∆v/t? Rearrange it to form at = ∆v. The units are (m/s2)s. The seconds cancel, leaving m/s, or velocity. So, Ft = m∆v, or Ft = ∆mv. This can also be derived from two equations relating to acceleration. a = F/m and a = ∆v/t. ...
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.