Slide 1
... 11.3 Center of Gravity Center of mass is often called center of gravity, the average position of all the particles of weight that make up an object. For almost all objects on and near Earth, these terms are interchangeable. There can be a small difference between center of gravity and center of mass ...
... 11.3 Center of Gravity Center of mass is often called center of gravity, the average position of all the particles of weight that make up an object. For almost all objects on and near Earth, these terms are interchangeable. There can be a small difference between center of gravity and center of mass ...
Slide 1
... The rotational inertia of a gymnast is up to 20 times greater when she is swinging in a fully extended position from a horizontal bar than after dismount when she somersaults in the tuck position. Rotation transfers from one axis to another, from the bar to a line through her center of gravity, and ...
... The rotational inertia of a gymnast is up to 20 times greater when she is swinging in a fully extended position from a horizontal bar than after dismount when she somersaults in the tuck position. Rotation transfers from one axis to another, from the bar to a line through her center of gravity, and ...
Chapter 6 Momentum Analysis of Flow Systems
... gage pressure at the inlet of the elbow and the anchoring force needed to hold the elbow in place are to be determined. Assumptions 1 The flow is steady and incompressible. 2 Frictional effects are negligible in the calculation of the pressure drop (so that the Bernoulli equation can be used). 3 The ...
... gage pressure at the inlet of the elbow and the anchoring force needed to hold the elbow in place are to be determined. Assumptions 1 The flow is steady and incompressible. 2 Frictional effects are negligible in the calculation of the pressure drop (so that the Bernoulli equation can be used). 3 The ...
Worked Examples from Introductory Physics Vol. I: Basic Mechanics
... with which one finishes up a problem. But the level of mathematics and calculator skills required in a general physics course is not very great. Any student who has difficulty solving the equations we derive in working these problems really needs to re–take some math courses! Physics is all about fi ...
... with which one finishes up a problem. But the level of mathematics and calculator skills required in a general physics course is not very great. Any student who has difficulty solving the equations we derive in working these problems really needs to re–take some math courses! Physics is all about fi ...
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.