Question

Mary is an avid game show fan and one of the contestants on a popular game show. She spins the wheel and after 1.5 revolutions the wheel comes to rest on a space that has a $1500.00 prize. If the initial angular speed of the wheel is 3.25 rad/s, find the angle through which the wheel has turned when the angular speed is1.60 rad/s.

Unit answer in rev.

Answer 1

`\theta =1.14\ rev`

Step-by-step explanation:

given,

θ = 1.5 revolution

initial angular speed = ωi = 3.25 rad/s

final angular speed = ωf = 1.60 rad/s

angular acceleration of the particle

`\alpha = (-\omega_i^2)/(2\theta)`

`\alpha = (-3.25^2)/(2* 1.5 * 2\pi\ rad)`

`\alpha =-0.56\ rad/s^2`

Angular displacement of the wheel

using rotational formula to calculate displacement

`\theta = (\omega_f^2-\omega_i^2)/(2\alpha)`

`\theta = (1.60^2-3.25^2)/(2* (-0.56))`

`\theta =7.14\ rad`

`\theta =7.14* (1)/(2\pi)`

`\theta =1.14\ rev`