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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).
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]
If this component is 0, the motion is uniform circular motion, and the velocity changes in direction only. The radial acceleration (perpendicular to direction of motion) is given by a R = v 2 r = ω 2 r . {\displaystyle a_{\mathrm {R} }={\frac {v^{2}}{r}}=\omega ^{2}r\,.}
In accordance with Newton's third law of motion, the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion. [40] [41] [42] [43]
The constancy of areal velocity may be illustrated by uniform circular and linear motion. In uniform circular motion, the particle moves with constant speed v around the circumference of a circle of radius r. Since the angular velocity ω = v/r is constant, the area swept out in a time Δt equals ω r 2 Δt; hence, equal areas are swept out in ...
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 ...
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 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).