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%u02DA. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.379 rev/s2 and the initial angular velocity is (a) +1.48 rev/s and (b) +2.14 rev/s.

Explanation / Answer

a)

acceleration = - 0.379 rev/s2

initial velocity (u ) = 1.48 rev/se

final velocity (v) = 0

v^2 = u^2 + 2 * a * s

so s = 1.48^2 / ( 2 * 0.379) = 2.89 revolution = 2.89 * 360 = 1,040.296 degree = 1040.296/30 divisions

= 34.686

so 34th division = 12*2 + 10

so number 11

b)

acceleration = - 0.379 rev/s2

initial velocity (u ) = 2.14 rev/se

final velocity (v) = 0

v^2 = u^2 + 2 * a * s

so s = 2.14^2 / ( 2 * 0.379) = 6.0417 revolution = 6.0417 * 360 = 2,175.008 degree =2,175.008/30 divisions

= 72.500

so 72nd division = 12*6 + 0

so number 1

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.