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Centripetal acceleration

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Centripetal acceleration is essentially the acceleration of an object in uniform circular motion, or the rate of change of tangential velocity where the acceleration vector is always directed towards the center of the circle formed. Essentially, tangential velocity is constant; however, the direction of the tangential velocity vector changes as the object rotates.

Roller coasterEdit

When trying to visualize centripetal acceleration in action, think of a roller coaster. As a roller coaster moves along on the track, centripetal and centrifugal forces are added. The centripetal force pushes towards the centre of an object to ensure that the coaster remains on the track. Centripetal force (a necessary net force) also ensures that the roller coaster remains on the track by combining centripetal force and regular acceleration to produce centripetal acceleration. The roller coaster is inclined to move in a straight line, it is also pushed into the track, thus producing an acceleration effect. Centrifugal force pushes outside of the tracks by opposing its opposite centripetal force, thus allowing the coaster to move in circular motion. In a roller coaster traveling in a loop or circle, your body is strapped into the roller coaster to move along with it in its circular path so as not to continue moving straight.....Centrifugal force does not exist. There is nothing "pushing" outward while an object negotiates a curve. The only forces acting on a roller coaster are weight and the force of the track pushing on the train. Using "sum of forces," you can then determine the acceleration of the train.

Uniform circular motionEdit

Objects moving in uniform circular motion have a centripetal acceleration directed towards the center of curvature of the path, have a magnitude proportional to the square of the velocity, and a magnitude inversely proportional to the path radius.


The following equations may be used to determine centripetal acceleration and its relationship to other variables.

ac = v2 / r
ac = 4∏2 r/ T2
ac = (2∏r/T) 2 /r


In another effort to test for centripetal acceleration, follow the simple procedure steps below.

Using a paper clip and a piece of string, and a small but heavy object such as a larger marble. Open the paper clip, tie the string to the end, and tie the object to the end of the string securely. Holding the empty end of the paper clip in one hand, gain momentum and twirl the object around your head in a circle.

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