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Newton's second law, in modern form, states that the time derivative of the momentum is the force: =. If the mass m {\displaystyle m} does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration: [ 22 ] F = m d v d t ...
So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion.
This means, in the case of Newton's second law, the right side would be in the form of , while in the Ehrenfest theorem it is in the form of . The difference between these two quantities is the square of the uncertainty in x {\displaystyle x} and is therefore nonzero.
The net force is the combined effect of all the forces on the object's acceleration, as described by Newton's second law of motion. When the net force is applied at a specific point on an object, the associated torque can be calculated.
The second law of thermodynamics may be expressed in many specific ways, [23] the most prominent classical statements [24] being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms ...
This appears to simply be an expression of Newton's second law (F = ma) in terms of body forces instead of point forces. Each term in any case of the Navier–Stokes equations is a body force. A shorter though less rigorous way to arrive at this result would be the application of the chain rule to acceleration:
The Wikidata item linked to this page is Newton's second law of motion for constant mass (Q2397319). Use this template only on hard redirects – for soft redirects use {{Soft redirect with Wikidata item}}.
A measurement of acceleration can be a scalar or a vector, but not both. Therefore, it's better to use "or" in the relevant sentence. Newton's second law is the statement F=ma. The statement 1 N = 1 kg · m s-2 is a special case, or example, of Newton's second law. Quotation marks are for quoting, not emphasis.