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If the mass 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] = =.
Analogous to mass times acceleration, the moment of inertia tensor I depends on the distribution of mass about the axis of rotation, and the angular acceleration is the rate of change of angular velocity, =.
hence the net force is equal to the mass of the particle times its acceleration. [ 1 ] Example : A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s.
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
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.
The jump in acceleration equals the force on the mass divided by the mass. That is, each time the mass passes through a minimum or maximum displacement, the mass experiences a discontinuous acceleration, and the jerk contains a Dirac delta until the mass stops.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
Proper acceleration reduces to coordinate acceleration in an inertial coordinate system in flat spacetime (i.e. in the absence of gravity), provided the magnitude of the object's proper-velocity [3] (momentum per unit mass) is much less than the speed of light c.