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rate of change
... The Lagrangian term dt is the rate of change experienced by a given tagged water parcel. The Eulerian term t is the local rate of change at a fixed point. du ...
... The Lagrangian term dt is the rate of change experienced by a given tagged water parcel. The Eulerian term t is the local rate of change at a fixed point. du ...
File
... total momentum before collision momentum = mass x velocity car: = 1000 kg x +20 m/s = +20000 kg m/s lorry: = 2000 kg x -16 m/s = -32000 kg m/s total initial momentum = -12000 kg m/s Momentum is conserved in the collision so total momentum after collision = -12000 kg m/s total momentum = total mass ...
... total momentum before collision momentum = mass x velocity car: = 1000 kg x +20 m/s = +20000 kg m/s lorry: = 2000 kg x -16 m/s = -32000 kg m/s total initial momentum = -12000 kg m/s Momentum is conserved in the collision so total momentum after collision = -12000 kg m/s total momentum = total mass ...
rotational inertia
... Rotational inertia, I , depends on mass and how that mass is distributed around the axis of rotation. The greater the distance between the bulk of the mass and the axis of rotation, the greater the rotational inertia. Spherical shell: the bulk of the mass is as far away from the axis as it ...
... Rotational inertia, I , depends on mass and how that mass is distributed around the axis of rotation. The greater the distance between the bulk of the mass and the axis of rotation, the greater the rotational inertia. Spherical shell: the bulk of the mass is as far away from the axis as it ...
Lecture 18
... Vector Nature of Angular Quantities • We can treat both ω and α as vectors • If we look at points on the wheel, they all have different velocities in the xy plane – Choosing a vector in the xy plane doesn’t make sense – Choose vector in direction of axis of rotation – But which direction? z ...
... Vector Nature of Angular Quantities • We can treat both ω and α as vectors • If we look at points on the wheel, they all have different velocities in the xy plane – Choosing a vector in the xy plane doesn’t make sense – Choose vector in direction of axis of rotation – But which direction? z ...
CHAPTERS 3 & 4
... The sum of two or more vectors. The order of adding the vectors does not matter, just like adding any other values. Since the vectors are drawn to scale, the magnitude of the resultant ( R ) can be measured with a ruler. ...
... The sum of two or more vectors. The order of adding the vectors does not matter, just like adding any other values. Since the vectors are drawn to scale, the magnitude of the resultant ( R ) can be measured with a ruler. ...
AP1 Momentum - APlusPhysics
... point is 20 m/s. Once the firecracker explodes, three pieces of equal mass are ejected. The vertical components of the velocity of the first and second pieces are equal in magnitude and opposite in direction, so the vertical component of velocity for the remaining piece must be zero. The horizontal ...
... point is 20 m/s. Once the firecracker explodes, three pieces of equal mass are ejected. The vertical components of the velocity of the first and second pieces are equal in magnitude and opposite in direction, so the vertical component of velocity for the remaining piece must be zero. The horizontal ...
here.
... • A point particle moving along a wire in the shape of a line or circle has one degree of freedom, namely its position (coordinate) along the wire. A point particle moving in a central force field has three degrees of freedom, we need three coordinates to specify the location of the particle. The Ea ...
... • A point particle moving along a wire in the shape of a line or circle has one degree of freedom, namely its position (coordinate) along the wire. A point particle moving in a central force field has three degrees of freedom, we need three coordinates to specify the location of the particle. The Ea ...
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.