Scalar and Vector Fields - METU | Department of Mechanical
... Hence, the equation for the velocity field (P) of points of the disk becomes r r r r r r r r v(P) = v(x,y,z) = ω k × (x i + y j + z k) = - ω y i + ω x j • Note that the vector function defined by the above equation can be evaluated mathematically for any point P(x,y,z) in the whole space. • However, ...
... Hence, the equation for the velocity field (P) of points of the disk becomes r r r r r r r r v(P) = v(x,y,z) = ω k × (x i + y j + z k) = - ω y i + ω x j • Note that the vector function defined by the above equation can be evaluated mathematically for any point P(x,y,z) in the whole space. • However, ...
BASICS OF CONTINUUM MECHANICS
... interacting objects. The total momentum will change also if there is exchange of matter with the outside of the system. The SI unit of momentum is kilograms meters/second (kg m.s-1). Basics in continuum mechanics ...
... interacting objects. The total momentum will change also if there is exchange of matter with the outside of the system. The SI unit of momentum is kilograms meters/second (kg m.s-1). Basics in continuum mechanics ...
Noether`s theorem
... We begin by recalling concepts learnt from previous lectures with the help of a simple example. Consider a particle of mass m moving under the influence of gravity and denote its height above the datum by q. That is, q will be the coordinate defining the position of the particle. We are interested i ...
... We begin by recalling concepts learnt from previous lectures with the help of a simple example. Consider a particle of mass m moving under the influence of gravity and denote its height above the datum by q. That is, q will be the coordinate defining the position of the particle. We are interested i ...
What is Reality? New Scientist
... various neutrinos streaming through us from the sun and other sources. Others, though, do not seem to be part of everyday reality, including the top and bottom quarks and the heavy, electron-like tau particle. "On the face of it, they don't play a role," says Paul Davies of Arizona State University ...
... various neutrinos streaming through us from the sun and other sources. Others, though, do not seem to be part of everyday reality, including the top and bottom quarks and the heavy, electron-like tau particle. "On the face of it, they don't play a role," says Paul Davies of Arizona State University ...
Read PDF - Physics (APS)
... that there are resolvable tidal forces across the spatial extent of the interferometer, then the wave function of an interfering particle can no longer be approximated as traveling along a single populated geodesic. Instead, the two arms follow separate trajectories that accelerate with respect to o ...
... that there are resolvable tidal forces across the spatial extent of the interferometer, then the wave function of an interfering particle can no longer be approximated as traveling along a single populated geodesic. Instead, the two arms follow separate trajectories that accelerate with respect to o ...
second-order linear homogeneous differential equations
... If there are no external forces acting on the system, then the object is said to have free motion and the motion of the object is completely determined by the displacement and velocity of the object at time t = 0, the stiffness of the spring as measured by the spring constant k, and the viscosity of ...
... If there are no external forces acting on the system, then the object is said to have free motion and the motion of the object is completely determined by the displacement and velocity of the object at time t = 0, the stiffness of the spring as measured by the spring constant k, and the viscosity of ...
f.pdf
... 10(20pts) (a) Find the work done by a force field F~ (x, y, z) = zi + xj + yk on an object moving on a line from (1, −2, 2) to (0, 3, −2). ...
... 10(20pts) (a) Find the work done by a force field F~ (x, y, z) = zi + xj + yk on an object moving on a line from (1, −2, 2) to (0, 3, −2). ...
Wave packet
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In physics, a wave packet (or wave train) is a short ""burst"" or ""envelope"" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating.Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation. It is possible to deduce the time evolution of a quantum mechanical system, similar to the process of the Hamiltonian formalism in classical mechanics. The dispersive character of solutions of the Schrödinger equation has played an important role in rejecting Schrödinger's original interpretation, and accepting the Born rule.In the coordinate representation of the wave (such as the Cartesian coordinate system), the position of the physical object's localized probability is specified by the position of the packet solution. Moreover, the narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the momentum of the wave. This trade-off between spread in position and spread in momentum is a characteristic feature of the Heisenberg uncertainty principle,and will be illustrated below.