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Newton's first law expresses the principle of inertia: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the status quo, but external forces can perturb this. The modern understanding of Newton's first law is that no inertial observer is privileged over any other.
The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [13]: 1112. The force in the equation is not the force the object exerts.
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: [2] 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.
Relative velocities between two particles in classical mechanics. The figure shows two objects A and B moving at constant velocity. The equations of motion are: = +, = +, where the subscript i refers to the initial displacement (at time t equal to zero).
The units and nature of each generalized momentum will depend on the corresponding coordinate; in this case p z is a translational momentum in the z direction, p s is also a translational momentum along the curve s is measured, and p φ is an angular momentum in the plane the angle φ is measured in. However complicated the motion of the system ...
The value (,) of the Hamiltonian is the total energy of the system, in this case the sum of kinetic and potential energy, traditionally denoted T and V, respectively. Here p is the momentum mv and q is the space coordinate.
Planck was able to calculate the value of from experimental data on black-body radiation: his result, 6.55 × 10 −34 J⋅s, is within 1.2% of the currently defined value. [2] He also made the first determination of the Boltzmann constant k B {\displaystyle k_{\text{B}}} from the same data and theory.
The motion of a particle (a point-like object) along a line can be described by its position , which varies with (time). An example of linear motion is an athlete running a 100-meter dash along a straight track. [2] Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net ...