Circular Motion - Humble Independent School District
Circular Motion r Fc, ac v Centripetal acceleration acceleration of an object in circular motion. It is directed toward the center of the circular path. 2 v ac = r ac = centripetal acceleration, m/s2 v = tangential speed, m/s
r = radius, m Centripetal Force the net inward force that maintains the circular motion of an object. Fc = m a c mv Fc = r 2 Fc = centripetal force, N m = mass, kg ac = centripetal acceleration, m/s2 v = tangential speed, m/s r = radius, m
For a constant tangential speed: v = tangential speed, m/s d 2r v= = t T d = distance, m t = time, s r = radius, m T = period, s T= 1 f
or f = 1 T T = period, s F = frequency, rev/s Period the time for one revolution Frequency number of revolutions per time Note: Period and frequency are inverses. Since centripetal force is a net force, there must be a force causing it. Some examples are
A car going around a curve on a flat road: Fc = Ff (friction force) Orbital motion, such as a satellite: Fc = Fg (weight or force of gravity) A person going around in a spinning circular room: Fc = FN (normal force) A mass on a string (horizontal circle, i.e.. parallel to the ground): Fc = T (tension in the string) For a mass on a string moving in a vertical circle, the centripetal force is due to different forces in different locations.
At the top of the circle, Fc = T + Fg (tension plus weight or gravity) At the bottom of the circle, Fc = T - Fg (tension minus weight or gravity) On the outermost side, Fc = T Anywhere other than above, you would need to find the component of gravity parallel to the tension and either add or subtract tension depending on the location on the circular path
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