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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
It concerns only variables derived from the positions of objects and time. In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the SUVAT equations, arising from the definitions of kinematic quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
The Lorentz force law provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. [ 79 ] : 85 According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge q ...
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
For a constant mass m, acceleration a is directly proportional to force F according to Newton's second law of motion: = In classical mechanics of rigid bodies, there are no forces associated with the derivatives of acceleration; however, physical systems experience oscillations and deformations as a result of jerk.
Also equations of motion can be formulated which connect acceleration and force. Equations for several forms of acceleration of bodies and their curved world lines follow from these formulas by integration. Well known special cases are hyperbolic motion for constant longitudinal proper acceleration or uniform circular motion.
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 expression relating force and acceleration for a particle with constant non-zero rest mass moving in the direction at velocity is: [59]: 216 = (,,), where = /. is called the Lorentz factor. The Lorentz factor increases steeply as the relative velocity approaches the speed of light.