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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: [ 21 ] F = m d v d t ...
Traditionally, thermodynamics has recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law. [1] [2] [3] A more fundamental statement was later labelled as the zeroth law after the first three laws had been established.
The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions.A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient).
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.
The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law or their derivative form, Lagrangian mechanics. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the ...
Since the definition of acceleration is a = dv/dt, the second law can be written in the simplified and more familiar form: =. So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle.
Using Newton's second law, the force exerted by a body (particle 2) on another body (particle 1) is: =. The force exerted by particle 1 on particle 2 is: = According to Newton's third law, the force that particle 2 exerts on particle 1 is equal and opposite to the force that particle 1 exerts on particle 2: =
So for a free particle, Newton's second law coincides with the geodesic equation and states that free particles follow geodesics, the extremal trajectories it can move along. If the particle is subject to forces F ≠ 0 , the particle accelerates due to forces acting on it and deviates away from the geodesics it would follow if free.