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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 ...
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 [ 6 ] 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 ...
e. In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p1, and a subsequent momentum is p2, the object has received an impulse J: Momentum is a vector quantity, so impulse is also a vector quantity. Newton’s second law of motion states that the rate of change ...
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.
If for example, the potential () is cubic, (i.e. proportional to ), then ′ is quadratic (proportional to ). This means, in the case of Newton's second law, the right side would be in the form of x 2 {\displaystyle \langle x\rangle ^{2}} , while in the Ehrenfest theorem it is in the form of x 2 {\displaystyle \langle x^{2}\rangle } .
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.
Consider Newton's second law, = where F is the sum of forces on the object, m is mass, and a is the acceleration. Newton's equation can be applied to the tangential axis only. This is because only changes in speed are of concern and the bob is forced to stay in a circular path.
It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time.