(b) What is Mary\'s tangential speed v M compared to that of Alex\'s tangential
ID: 1312533 • Letter: #
Question
(b) What is Mary's tangential speed vM compared to that of Alex's tangential speed vA? Give your answer as a multiple of vA.
(a) What is Mary's angular speed ?M compared to that of Alex's angular speed ?A? Give your answer as a multiple of ?A
Mary and her younger brother Alex decide to ride the 26-foot-diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 11 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 7 feet from the center.
Explanation / Answer
A. Angular speed is not affected by the differences in their distance. Angular speed is the magnitude of angular velocity which is the change in the angle (?) over the change in time (t). Since the change in their angle over time is the same, their magnitude must also be the same. So that means that wM = 1wA
B. The tangential speed does in fact change with the distance. To find tangential speed you use the formula 2?r/T where T is the period and r is the radius. Mary's tangential speed is 2?(r1)/T and Alex's is 2?(r2). The multiple is found simply by taking r1/r2. This means that Mary's speed is 11/7 times greater than Alex's speed.
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