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By a transformation of variables, [14] any central-force problem can be converted into an equivalent parallel-force problem. [ note 6 ] In place of the ordinary x and y Cartesian coordinates, two new position variables ξ = x / y and η = 1/ y are defined, as is a new time coordinate τ τ = ∫ d t y 2 {\displaystyle \tau =\int {\frac {dt}{y ...
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking) of the class of objects to which it belongs.
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
4–5×10 4 J: Energy released by the combustion of 1 gram of gasoline [106] 5×10 4 J: Kinetic energy of 1 gram of matter moving at 10 km/s [107] 10 5 3×10 5 – 15×10 5 J: Kinetic energy of an automobile at highway speeds (1 to 5 tons [108] at 89 km/h or 55 mph) [109] 5×10 5 J Kinetic energy of 1 gram of a meteor hitting Earth [110]
So are 1 and 2, 1 and 9, or 1 and 0.2. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors of ten). [2]
10 4 N 16.5 kN The bite force of a 5.2 m (17 ft) saltwater crocodile [20] 18 kN The estimated bite force of a 6.1 m (20 ft) adult great white shark [21] 25 kN Approximate force applied by the motors of a Tesla Model S during maximal acceleration [22] 25.5 to 34.5 kN The estimated bite force of a large 6.7 m (22 ft) adult saltwater crocodile [23]
is the charge density measured by an inertial observer O who sees the electric current moving at speed u (the magnitude of the 3-velocity); ρ 0 {\displaystyle \rho _{0}} is “the rest charge density”, i.e., the charge density for a comoving observer (an observer moving at the speed u - with respect to the inertial observer O - along with ...
An overview of ranges of mass. To help compare different orders of magnitude, the following lists describe various mass levels between 10 −67 kg and 10 52 kg. The least massive thing listed here is a graviton, and the most massive thing is the observable universe.