*73.  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 30.0°. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.200 rev/s2 and the initial angular velocity is (a) +1.20 rev/s and (b) +1.47 rev/s.

 

 

We know wheel is decelerating so a < 0, hence the minus sign above.  Solve for q

 

For initial angular velocity in part (a)

 

 

For initial angular velocity in part (b)

 

 

Whole revolutions put the wheel back at the starting point.  Find the angular displacement into degrees.  First remove the whole revolutions.

 

 

So now find out how many 30° segments we are at

 

So 7 full 30° segments have been crossed so we are in the 8th one, so section #8

 

Repeat for the b angular velocity

 

 

So now find out how many 30° segments we are at

 

So 4 full 30° segments have been crossed so we are in the 5th one, so section #5

 

 

 

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This page last updated on January 11, 2020