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Uniform circular motion is the movement of an object or particle trajectory at a constant speed around a circle with a fixed radius The positions of an object in uniform circular motion, relative to the center of the circle, are given by the position vectors r1 and r2, shown in Figure 6-5a As the object moves around the circle, the length of each position vector does not change, but its direction does To find the object s velocity, you need to find its displacement vector over a time interval The change in position, or the object s displacement, is represented by r Figure 6-5b shows two position vectors: r1 at the beginning of a time interval, and r2 at the end of the time interval Remember that a position vector is a displacement vector with its tail at the origin In the vector diagram, r1 and r2 are subtracted to give the resultant r, the displacement during the time interval You know that a moving object s average velocity is d/ t, so for an object in circular motion, v r/ t The velocity vector has the same direction as the displacement, but a different length You can see in Figure 6-6a that the velocity is at right angles to the position vector, which is tangent to its circular path As the velocity vector moves around the circle, its direction changes but its length remains the same What is the direction of the object s acceleration Figure 6-6a shows the velocity vectors v1 and v2 at the beginning and end of a time interval The difference in the two vectors, v, is found by subtracting the vectors, as shown in Figure 6-6b The average acceleration, a v/ t, is in the same direction as v; that is, toward the center of the circle Repeat this process for several other time intervals when the object is in different locations on the circle As the object moves around the circle, the direction of the acceleration vector changes, but its length remains the same Notice that the acceleration vector of an object in uniform circular motion always points in toward the center of the circle For this reason, the acceleration of such an object is called center-seeking or centripetal acceleration.



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" Educating the Net Generation " by Diana Oblinger, James L ...
The Net Generation has grown up with information technology. The aptitudes ... Located in Drake Library as an eBook (For PDF , see above link. For HTML or ...

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18 Mar 2019 ... NET wrapper around the popular wkhtmltopdf library and we will use it to convert an HTML template to a PDF document. Things that make this ...

Figure 6-5 The displacement, r, of an object in circular motion, divided by the time interval in which the displacement occurs, is the object s average velocity during that time interval

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Answer (for Objective 53): E is correct BeemerdoStuff() will not compile because it s attempting to override using a weaker access modifier A, B, C, D, and F are incorrect based on the above

Figure 6-6 The direction of the change in velocity is toward the center of the circle, and so the acceleration vector also points to the center of the circle





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What is the magnitude of an object s centripetal acceleration Compare the triangle made from the position vectors in Figure 6-5b with the triangle made by the velocity vectors in Figure 6-6b The angle between r1 and r2 is the same as that between v1 and v2 Therefore, the two triangles formed by subtracting the two sets of vectors are similar triangles, and the ratios of the lengths of two corresponding sides are equal Thus, r/r v/v The equation is not changed if both sides are divided by t

Space Elevators Scientists are considering the use of space elevators as a low-cost transportation system to space A cable would be anchored to a station at Earth s equator, and the cable would extend almost 35,800 km from Earth s surface The cable would be attached to a counterweight and would stay extended due to centripetal force Special magnetically powered vehicles would then travel along the cable

Solve this equation for acceleration and give it the special symbol ac , for centripetal acceleration

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