Question

Mary is an avid game show fan and one of the contestants on a popular game show. She spins the wheel, and after 5.5 revolutions, the wheel comes to rest on a space that has a $1500 value prize. If the initial angular speed of the wheel is 3.50 rad/s, find the angle through which the wheel has turned when the angular speed reaches 2.00 rad/s.

Answer 1

Answer:

Explanation:

Given

after 5.5 revolution wheel comes to stop

i.e. radian turned before stopping

$\theta =2\pi \times 5.5 rad$

initial angular velocity $\omega _0=3.5 rad/s$

$\omega ^2-\omega _0^2=2\cdot \alpha \cdot \theta$

where  $\alpha =angular\ acceleration\ or\ deceleration$                                                                                                                                                                                                                                                                                                    

$0-(3.5)^2=2(\alpha )(2\pi \cdot 5.5)$

$\alpha =-0.1772 rad/s^2$

angle turned when final angular velocity is $2 rad/s$

$2^2-3.5^2=2\cdot (-0.1772)(\theta )$

$\theta =23.27\ radians$