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Solving applications dealing with non-uniform circular motion involves force analysis. With a uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In a non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration.
A ball in circular motion held by a string tied to a fixed post. The figure at right shows a ball in uniform circular motion held to its path by a string tied to an immovable post. In this system a centripetal force upon the ball provided by the string maintains the circular motion, and the reaction to it, which some refer to as the reactive ...
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]
In considering a solitary globe, all forms of motion, uniform and accelerated, are unobservable in an otherwise empty universe. [17] This notion was followed up in modern times by Ernst Mach. For a single body in an empty universe, motion of any kind is inconceivable. Because rotation does not exist, centrifugal force does not exist.
In uniform circular motion, that is moving with constant speed along a circular path, a particle experiences an acceleration resulting from the change of the direction of the velocity vector, while its magnitude remains constant. The derivative of the location of a point on a curve with respect to time, i.e. its velocity, turns out to be always ...
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]
A classic example of a fictitious force in circular motion is the experiment of rotating spheres tied by a cord and spinning around their centre of mass. In this case, the identification of a rotating, non-inertial frame of reference can be based upon the vanishing of fictitious forces.
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