Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel a
ID: 1280807 • Letter: M
Question
Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 8 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 5 feet from the center.
(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.
(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.
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 r1/r2 times greater (or lesser depending on the values of the radii) than Alex's speed. Those values weren't included in your question so you can figure that out.
vm/va=rm/ra=8/5
Vm=1.6 Va