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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 ...
Some definitions and concepts from classical mechanics do carry over to SR, such as force as the time derivative of momentum (Newton's second law), the work done by a particle as the line integral of force exerted on the particle along a path, and power as the time derivative of work done. However, there are a number of significant ...
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference , but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change.
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.
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.
The Buridan impetus theory developed one of the most important thought experiments in the history of science, the 'tunnel-experiment'. This experiment incorporated oscillatory and pendulum motion into dynamical analysis and the science of motion for the first time. It also established one of the important principles of classical mechanics.
In Newtonian mechanics, for one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, can be obtained by means of Newton's second law and Hooke's law for a mass on a spring.
Nearly a century later, Isaac Newton had formulated his three laws of motion. In particular, Newton's second law states that a force F applied to a mass m produces an acceleration a given by the equation F=ma. Newton then posed the question: what must the force be that produces the elliptical orbits seen by Kepler?