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

Step-by-step explanation:

Given

after 5.5 revolution wheel comes to stop

i.e. radian turned before stopping

`\theta =2\pi * 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`