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In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.
Energy can broadly be classified into kinetic, due to a body's motion, and potential, due to a body's position relative to others. Thermal energy, the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made.
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.
The kinetic energy of an object is equal to the work, or force in the direction of motion times its displacement , needed to accelerate the object from rest to its given speed. The same amount of work is done by the object when decelerating from its current speed to a state of rest.
The force is perpendicular to the relative direction of motion and oriented towards the direction of rotation, i.e. the direction the "nose" of the ball is turning towards. [7] The magnitude of the force depends primarily on the rotation rate, the relative velocity, and the geometry of the body; the magnitude also depends upon the body's ...
In accordance with Newton's third law of motion, the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion. [40] [41] [42] [43]
Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space.This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession.
The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.