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In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed , or non-uniform with a changing rate of rotation.
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.
Tangential speed is the speed of an object undergoing circular motion, i.e., moving along a circular path. [1] A point on the outside edge of a merry-go-round or turntable travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed ...
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]
Coupled pendulums can affect each other's motion, either through a direction connection (such as a spring connecting the bobs) or through motions in a supporting structure (such as a tabletop). The equations of motion for two identical simple pendulums coupled by a spring connecting the bobs can be obtained using Lagrangian mechanics.
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 Coriolis parameter typically has a mid-latitude value of about 10 −4 s −1; hence for a typical atmospheric speed of 10 m/s (22 mph), the radius is 100 km (62 mi) with a period of about 17 hours. For an ocean current with a typical speed of 10 cm/s (0.22 mph), the radius of an inertial circle is 1 km (0.6 mi).
Substituting in the Lagrangian L(q, dq/dt, t) gives the equations of motion of the system. The number of equations has decreased compared to Newtonian mechanics, from 3N to n = 3N − C coupled second-order differential equations in the generalized coordinates. These equations do not include constraint forces at all, only non-constraint forces ...