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Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration has two terms, a combination known as a total or material derivative. The mass of an infinitesimal portion depends upon the fluid density , and there is a net force upon it if the fluid pressure varies from one side of it to another.
The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. [5] It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.
In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it (Newton's second law): = =, where F is the net force acting on the body, m is the mass of the body, and a is the center-of-mass acceleration.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
By Newton's second law, the cause of acceleration is a net force acting on the object, which is proportional to its mass m and its acceleration. The force, usually referred to as a centripetal force , has a magnitude [ 7 ] F c = m a c = m v 2 r {\displaystyle F_{c}=ma_{c}=m{\frac {v^{2}}{r}}} and is, like centripetal acceleration, directed ...
Likewise, Newton's second law of motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body: =, where I {\displaystyle I} is the moment of inertia of the body
For completeness, the inertial acceleration due to impressed external forces can be determined from the total physical force in the inertial (non-rotating) frame (for example, force from physical interactions such as electromagnetic forces) using Newton's second law in the inertial frame: = Newton's law in the rotating frame then becomes