# PURPOSE - PURPOSE OBJECTIVES The purpose of this experiment...

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PURPOSE/ OBJECTIVES The purpose of this experiment is to study uniform circular motion and to compare the observed value of the centripetal force with the calculated value. APPARATUS/EQUIPMENT 1. Centripetal force apparatus 2. Motor with coupler and means for counting turns (Procedure A only) 3. Stopwatch or stop clock 4. Supporting rods, hook, right-angle clamp, and bench clamp (Procedure A only) 5. Weight hanger and weights 6. Vernier caliper (Procedure A only) 7. Level (Procedure B only) 8. Triple-beam balance (Procedure B only) THEORY If a body moves with constant speed in a circle, it is said to be moving with uniform circular motion. Even though the speed is constant, the velocity is continuously changing because the direction of the motion is continuously changing. Thus, such a body has an acceleration. It can be shown that the direction of the acceleration is always toward the center of the circle (because it is only the direction and not the magnitude of the velocity that is changing) and that its magnitude is given by r v a 2 where v is the speed of the body in meters per second and r is the radius of the path in meters. A force is necessary to produce this acceleration. Because it must be in the same direction as the acceleration-namely, toward the center of the circle as noted above-it is called centripetal force. Newton's second law now requires that the magnitude of this force be equal to the mass times the acceleration produced, so that in our present case
r v m F 2 where F is the force in newtons, m is the mass of the rotating body in kilograms, and v and r are the same as before. But by Newton's third law of motion, an equal and opposite force is exerted by the body on the restraining medium. This reaction is called centrifugal force. The centripetal force can also be expressed in terms of the angular speed, since v = rω and ω=2πf where v is the linear speed and r the radius of the path as before,  is the angular speed in radians per second, and f is the number of revolutions per second. Thus, F = mrwω 2 or F = 2 f 2 m where F is the centripetal force in newtons as already described. Figure () Centripetal force apparatus, manual form Apparatus for the experiment is shown in Fig. (). A stretched string provides the centrifugal force to keep the rotating mass moving in a circle, but the complete assembly is mounted on a horizontal bar (the rotating platform) mounted on a vertical shaft carried in very good bearings. A knurled portion of the shaft provides a convenient grip for the experimenter's fingers, and you'll find with a little practice that you can keep the assembly rotating at a constant speed quite accurately. Note that at the bottom of the spring there is a small pink disk, and because the spring and disk are at the center of rotation, the position of the latter is easily observed even with the apparatus in motion. The mass to be kept rotating at a particular radius is suspended by threads from a post mounted on the rotating platform at that