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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.
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 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 ...
For an object in uniform circular motion, the net force acting on the object equals: [46] = ^, where is the mass of the object, is the velocity of the object and is the distance to the center of the circular path and ^ is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object ...
Simple harmonic motion can be considered the one-dimensional projection of uniform circular motion. If an object moves with angular speed ω around a circle of radius r centered at the origin of the xy-plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.
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 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 ...
It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.