Kinetic energyIn physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
Newton's laws of motionNewton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. When a body is acted upon by a force, the time rate of change of its momentum equals the force. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
Newton's law of universal gravitationNewton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
Work (physics)In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when applied it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.
Newton's cannonballNewton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World). Newton's original plan for Philosophiæ Naturalis Principia Mathematica was that it should consist of two books, the first analyzing basic laws of motion, and the second applying them to the Solar System.
Euler's laws of motionIn classical mechanics, Euler's laws of motion are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws. Euler's first law states that the rate of change of linear momentum p of a rigid body is equal to the resultant of all the external forces Fext acting on the body: Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect.
Rotational energyRotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed: where The mechanical work required for or applied during rotation is the torque times the rotation angle. The instantaneous power of an angularly accelerating body is the torque times the angular velocity.
Kepler's laws of planetary motionIn astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. The three laws state that: The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Scalar multiplicationIn mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector—without changing its direction. The term "scalar" itself derives from this usage: a scalar is that which scales vectors.
Gauss's law for gravityIn physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's law for gravity is often more convenient to work from than Newton's law. The form of Gauss's law for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations.
Primary energyPrimary energy (PE) is the energy found in nature that has not been subjected to any human engineered conversion process. It encompasses energy contained in raw fuels and other forms of energy, including waste, received as input to a system. Primary energy can be non-renewable or renewable. Primary energy is used in energy statistics in the compilation of energy balances, as well as in the field of energetics. In energetics, a primary energy source (PES) refers to the energy forms required by the energy sector to generate the supply of energy carriers used by human society.
Energy developmentEnergy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include the production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reuse of energy that would otherwise be wasted. Energy conservation and efficiency measures reduce the demand for energy development, and can have benefits to society with improvements to environmental issues.
Dot productIn mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more).
Energy policyEnergy policy is the manner in which a given entity (often governmental) has decided to address issues of energy development including energy conversion, distribution and use as well as reduction of greenhouse gas emissions in order to contribute to climate change mitigation. The attributes of energy policy may include legislation, international treaties, incentives to investment, guidelines for energy conservation, taxation and other public policy techniques. Energy is a core component of modern economies.
Energy transitionAn energy transition (or energy system transformation) is a significant structural change in an energy system regarding supply and consumption. Currently, a transition to sustainable energy (mostly renewable energy) is underway to limit climate change. It is also called renewable energy transition. The current transition is driven by a recognition that global greenhouse-gas emissions must be drastically reduced. This process involves phasing-down fossil fuels and re-developing whole systems to operate on low carbon electricity.
Inner product spaceIn mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in . Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates.
Scalar (physics)In physics, scalars (or scalar quantities) are physical quantities that are unaffected by changes to a vector space basis (i.e., a coordinate system transformation). Scalars are often accompanied by units of measurement, as in "10cm". Examples of scalar quantities are mass, distance, charge, volume, time, speed, and the magnitude of physical vectors in general (such as velocity). A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change.
Energy povertyEnergy poverty is lack of access to modern energy services. It refers to the situation of large numbers of people in developing countries and some people in developed countries whose well-being is negatively affected by very low consumption of energy, use of dirty or polluting fuels, and excessive time spent collecting fuel to meet basic needs. Today, 759 million people lack access to consistent electricity and 2.6 billion people use dangerous and inefficient cooking systems.
Product (mathematics)In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together). When one factor is an integer, the product is called a multiple. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication.
Scalar (mathematics)A scalar is an element of a field which is used to define a vector space. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers).
