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Velocity and acceleration in non-uniform circular motion. In non-uniform circular motion, an object moves in a circular path with varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration. The net acceleration is directed towards the interior of the circle (but does not pass through its center).
This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and is measured in SI units as meters per second (m/s).
Stated formally, in general, an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = dr / dt ), and its acceleration (the second derivative of r, a = d 2 r / dt 2 ), and time t. Euclidean vectors in 3D are denoted throughout in bold.
The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).
Tangential speed is the speed of an object undergoing circular motion, i.e., moving along a circular path. [6] 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 ...
The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.. In the simplest case of circular motion at radius , with position given by the angular displacement () from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: =.
The speed in the formula is squared, so twice the speed needs four times the force, at a given radius. This force is also sometimes written in terms of the angular velocity ω of the object about the center of the circle, related to the tangential velocity by the formula v = ω r {\displaystyle v=\omega r} so that F c = m r ω 2 ...
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.