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The first of Newton's laws of motion states that an object's inertia keeps it in motion; since the object in the air has a velocity, it will tend to keep moving in that direction. A varying angular speed for an object moving in a circular path can also be achieved if the rotating body does not have a homogeneous mass distribution.
The term "radial motion" signifies the motion towards or away from the center of force, whereas the angular motion is perpendicular to the radial motion. Isaac Newton derived this theorem in Propositions 43–45 of Book I of his Philosophiæ Naturalis Principia Mathematica , first published in 1687.
A circular orbit is depicted in the top-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy remains constant throughout the constant speed circular orbit.
Newton's cannonball is a thought experiment that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward ...
Newton's first law requires that any body moving along any path other than a straight line be subject to a net non-zero force, and the free body diagram shows the force upon the ball (center panel) exerted by the string to maintain the ball in its circular motion. Newton's third law of action and reaction states that if the string exerts an ...
These results agree with those above for nonuniform circular motion. See also the article on non-uniform circular motion. If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force. [22]
For Huygens and Newton centrifugal force was the result of a curvilinear motion of a body; hence it was located in nature, in the object of investigation. According to a more recent formulation of classical mechanics, centrifugal force depends on the choice of how phenomena can be conveniently represented.
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.