SOLUTION: You are cycling with your friends every Saturday. You notice that the wheels of your bike make 12 revolutions in 14 seconds. (a) What is the average angular speed of the wheel in r

Algebra ->  Test -> SOLUTION: You are cycling with your friends every Saturday. You notice that the wheels of your bike make 12 revolutions in 14 seconds. (a) What is the average angular speed of the wheel in r      Log On


   

Question 1186511: You are cycling with your friends every Saturday. You notice that the wheels of your bike make 12 revolutions in 14 seconds. (a) What is the average angular speed of the wheel in radians/second (rad/s)? (b) What distance in meters (m) does the wheel travel if its radius is 35 cm?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)  The angular velocity is  w = %2812%2A%282pi%29%29%2F14 = %2812%2A%282%2A3.14%29%29%2F14 = 5.383 radians per second.


    +-----------------------------------------------------------------+
    |    You take the full rotation angle  12%2A%282%2Api%29  radians         |
    |    of 12 rotations, and divide it by the time of 14 seconds.    |
    +-----------------------------------------------------------------+



(b)  The distance = w*R = 5.383 * 0.35 = 1.884 m/s.


     +----------------------------------------------------------------+
     |   You take the angular velocity and multiply it by the radius. |
     +----------------------------------------------------------------+

Solved and carefully/thoroughly explained.