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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.
Continuous vortex sheet approximation by panel method. Roll-up of a vortex sheet due to an initial sinusoidal perturbation. Note that the integral in the above equation is a Cauchy principal value integral. The initial condition for a flat vortex sheet with constant strength is (,) =. The flat vortex sheet is an equilibrium solution.
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.
Every central force can produce uniform circular motion, provided that the initial radius r and speed v satisfy the equation for the centripetal force = () If this equation is satisfied at the initial moments, it will be satisfied at all later times; the particle will continue to move in a circle of radius r at speed v forever.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
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 ...
There are three Kinematic equations for linear (and generally uniform) motion. These are v = u + at; v 2 = u 2 + 2as; s = ut + 1 / 2 at 2; Besides these equations, there is one more equation used for finding displacement from the 0th to the nth second. The equation is: = + ()
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.