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What are Newton's 1st 2nd and 3rd laws of motion?
Newton's First Law. Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.
What is difference between magnitude and direction?
The significance of 'direction' can be seen in the difference between velocity and speed. In physics, speed is a pure scalar, or something with a magnitude but no direction --such as 5 m/s. On the other hand, velocity, in Physics, must be expressed as a vector with both a magnitude and a direction.
What is difference between kinetic friction and static friction?
The coefficient of static friction, typically denoted as μs, is usually higher than the coefficient of kinetic friction. The Force of Static Friction keeps a stationary object at rest! Once the Force of Static Friction is overcome, the Force of Kinetic Friction is what slows down a moving object!
The kinetic friction is usually not greater than the applied force. You start moving an object which increases the static force to prevent any motion. However, you keep applying more force until you reach a maximum value for the static friction. Then, the object begins to move.
What is contour integration in complex analysis?
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related to the calculus of residues, a method of complex analysis.
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/). It takes a function of a real variable t (often time) to a function of a complex variable s (complex frequency). The Laplace transform is very similar to the Fourier transform.
In mathematics and engineering, the s-plane is the complex plane on which Laplace transforms are graphed. It is a mathematical domain where, instead of viewing processes in the time domain modeled with time-based functions, they are viewed as equations in the frequency domain.
Control Systems: Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, ( named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.
Is centripetal force fictitious?
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) directed away from the axis of rotation that appears to act on all objects when viewed in a rotating frame of reference. A fictitious force is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.
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What force causes centripetal acceleration?
The direction of the net force is in the same direction as the acceleration. So for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. This is sometimes referred to as the centripetal force requirement.
The Four Fundamental Forces and their strengths
Gravitational Force – Weakest force; but infinite range. ( Not part of standard model)
Weak Nuclear Force – Next weakest; but short range.
Electromagnetic Force – Stronger, with infinite range.
Strong Nuclear Force – Strongest; but short range.
What are the 4 known forces of nature?
According to the present understanding, there are four fundamental interactions or forces: gravitation, electromagnetism, the weak interaction, and the strong interaction.
In physics, the fifth force is a proposed fundamental force, additional to the four known fundamental forces of nature.
What is the relationship between momentum and impulse?
Momentum is mass in motion, and any moving object can have momentum. An object's change in momentum is equal to its impulse. Impulse is a quantity of force times the time interval.
In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. From a geometrical perspective, it is a special case of the generalized Stokes' theorem.
What are the 4 types of Chemical Bonds?
Ionic bond: bond in which one or more electrons from one atom are removed and attached to another atom, resulting in positive and negative ions which attract each other. Other types of bonds include covalent bonds, metallic bonds and hydrogen bonding.
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What is the difference between ionic covalent and metallic bonds?
Ionic bonding occurs when transfer of electrons takes place. One atom (or molecule) donates one or more electrons to another. The ions then attract each other through electrostatic forces of attraction as they are oppositely charged.
Most compounds with ionic bonding, e.g. metal salts, dissolve in water. The oxygen atoms of water molecules are attracted to cations (ions with a positive charge) and water molecules surround it. This time it is the positive ends of the water molecule, the hydrogen atoms, that are attracted to the anion.
What happens when an ionic compound mixes with water and separates?
This should help you to picture what happens to salt as it dissolves in water. Salt is made up of sodium and chloride ions held together by ionic bonds. As the sodium and chloride ions move between the water molecules, the hydrogen bonds holding the water molecules together must also be broken.
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
What is an essential singularity?
The point a is called an essential singularity of the function f if the singularity is neither a pole nor a removable singularity. For example, the function f(z) = e1/z has an essential singularity at z = 0.
What is the residue of a complex function?
Residue (complex analysis) From Wikipedia, the free encyclopedia. In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
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In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function. This terminology comes from the Ancient Greek meros (μέρος), meaning "part," as opposed to holos (ὅλος), meaning "whole."
What is a singularity of a function?
In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities are extremely important in complex analysis, where they characterize the possible behaviors of analytic functions.
Eigenvalues and Eigenfunctions
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R where U is an open subset of Rn that satisfies Laplace's equation.
In mathematics, the Laurent series of a complex function f is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in a paper written in 1841, but it was not published until after his death.
Curl theorem The curl of a vector field measures the tendency for the vector field to swirl around. Imagine that the vector field represents the velocity vectors of water in a lake.
In physics, Green's theorem finds many applications. One of which is solving two-dimensional flow integrals, stating that the sum of fluid outflows from a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
Golgi staining was used by Spanish neuroanatomist Santiago Ramón y Cajal (1852–1934) to discover a number of novel facts about the organization of the nervous system, inspiring the birth of the neuron doctrine. Ultimately, Ramon y Cajal improved the technique by using a method he termed "double impregnation." Ramon y Cajal's staining technique, still in use, is called Cajal's Stain. Golgi's method is a silver staining technique that is used to visualize nervous tissue under light microscopy. The method was discovered by Camillo Golgi, an Italian physician and scientist, who published the first picture made with the technique in 1873.
Likened to the cell's "Post Office", the Golgi Apparatus modifies, sorts, and packages proteins for secretions.
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What does an ESCO do?
An energy service company (ESCO) is a commercial or non-profit business providing a broad range of energy solutions including designs and implementation of energy savings projects, retrofitting, energy conservation, energy infrastructure outsourcing, power generation and energy supply, and risk management.
The Small Business Innovation Research (or SBIR) program is a United States Government program, coordinated by the Small Business Administration, intended to help certain small businesses conduct research and development (R&D). Funding takes the form of contracts or grants.
