At a county fair there is a betting game that involves a spinning wheel. As the

Question

At a county fair there is a betting game that involves a spinning wheel. As the drawing shows, the wheel is set into rotational motion with the beginning of the angular section labeled "1" at the marker at the top of the wheel. The wheel then decelerates and eventually comes to a halt on one of the numbered sections. The wheel in the drawing is divided into twelve sections, each of which is an angle of 30. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.217 rev/s2 and the initial angular velocity is (a) +1.48 rev/s and (b) +2.74 rev/s.

rad/sNo unitsrad/s^2smradNJ

NsJmNo unitsrad/s^2radrad/s

Explanation / Answer

Convert everything to the same units - either degrees, or revs. I pick revs.

Each section is 30/360 = 1/12 of a rev.
Deceleration is 0.217 rev/s^2 so,

a) Initial =1.48 rev/s. Time to stop = 1.48/0.217 = 6.82 s. Distance traveled = (at^2)/2 = (0.217)46.5/2 = 5.04 revs, so it will stop on the same section it started - section 1.

b)Initial =2.74 rev/s. Time to stop = 2.74/0.217 = 12.63 s. Distance traveled = (at^2)/2 = (0.217)159.5/2 = 17.3 revs which is 17.3 revs + 3 sections, so it will stop on section 4.

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