Jason is lucky enough to be selected to take part in a Wheel of Fortune game. The Wheel of Fortune, which is 46.0 cm in radius, comprises 8 equal segments with only 3 prizes, i.e. a smartphone, a laptop, and a $100 cash as shown in Figure 2. With the starting position of the black pointer at the border of red and yellow segments, Jason spins the Wheel of Fortune with an initial tangential speed of 5.80 m/s in a clockwise direction. It is found that the Wheel of Fortune is slowing down at a rate of 1.05 rad/s². Determine (i) the initial angular speed of the wheel, and the time the wheel will remain spinning,  (ii) the angular displacement of the wheel,  (iii) which segment the pointer will point at when the wheel stops

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter3: Motion In Two Dimensions
Section: Chapter Questions
Problem 30P: A point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of...
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Jason is lucky enough to be selected to take part in a Wheel of Fortune game. The Wheel of Fortune, which is 46.0 cm in radius, comprises 8 equal segments with only 3 prizes, i.e. a smartphone, a laptop, and a $100 cash as shown in Figure 2. With the starting position of the black pointer at the border of red and yellow segments, Jason spins the Wheel of Fortune with an initial tangential speed of 5.80 m/s in a clockwise direction. It is found that the Wheel of Fortune is slowing down at a rate of 1.05 rad/s².

Determine
(i) the initial angular speed of the wheel, and the time the wheel will remain spinning, 
(ii) the angular displacement of the wheel, 
(iii) which segment the pointer will point at when the wheel stops

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