Circular Motion Essay

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CIRCULAR MOTION I. II. Uniform Circular Motion - motion in a circle at a constant speed A car moving in a circular path at a constant speed of 40km/h is an example of object in uniform circular motion. This means that at every point in the circle, the car would be moving at 40km/h. *Velocity is ALWAYS tangent to the circle, because at any instant the tangent specifies the direction of motion. The magnitude of the velocity vectors, corresponding to the speeds vA and vB, are equal. What is this uniform speed? The speed of the object is the distance it covers (here, 2πr) divided by time (here, T). In symbols, v=2πrT. Period (T) - time needed by an object in uniform circular motion to complete an orbit Distance - circumference of the circle with radius r, given as 2πr. Frequency (f) - no. of revolutions completed by a body in uniform circular motion per unit time To find the relation between f and T, let us start with this formula Distance = Velocity x Time Considering a circle as a path of the body, 2πr = vT But the velocity is also the number of revolutions made per unit time times the number of revolutions completed. v = f (2πr) Substituting this in the first equation gives f = 1T T = 1f 2πr = f (2πr) T 1 = fT Thus we derive the relationship between f and T. f = 1 T T = 1f Clearly in the figure, velocity changes from A to B, then from B to C. The change in velocity is denoted by v. Thus from A to B, v = vB - vA A change in velocity implies acceleration, i.e. a = vB - vAtB - tA To calculate acceleration of uniform circular motion, a= v2r a= 4π2rT2 a= 4π2rf2. Example 1 A body is fastened to a string 0.75 m long and is whirled to make 2 revolutions per second on a horizontal plane with the other end of the string as a center. Find the acceleration. Solution: r = 0.75 m , f = 2 rev

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