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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.
The last part of the book returns to the design of a clock where the motion of the pendulum is circular, and the string unwinds from the evolute of a parabola. It ends with thirteen propositions regarding bodies in uniform circular motion, without proofs, and states the laws of centrifugal force for uniform circular motion. [23]
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 ...
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.
In a vector field describing the linear velocities of each part of a rotating disk in uniform circular motion, the curl has the same value at all points, and this value turns out to be exactly two times the vectorial angular velocity of the disk (oriented as usual by the right-hand rule).
Vector contributions from the gravitational force (medium gray) and the gradient of the pressure (black) come together in an amazing way to produce the uniform circular motion of the fluid particles. For uniform circular motion, the net force (light gray) has constant magnitude and always points towards the center of the circle.
The set of all solutions to the above equation of motion consists of both circular trajectories and ellipse-shaped trajectories. All the solutions have the same period of revolution. This is a distinctive feature of motion under the influence of a harmonic force; all trajectories take the same amount of time to complete a revolution.
Non-uniform circular motion – Object movement along a circular path Thomson problem – Max distance configuration for N points on a sphere Uniform circular motion – Object movement along a circular path Pages displaying short descriptions of redirect targets