Answer:
The total number of revolution is 50 rev.
Explanation:
Given that,
Angular speed = 5.0 rev/s
Time = 8.0 s
We need to calculate the angular acceleration
Using equation of angular motion
![\omega_{f}-\omega_{i}=\alpha t](https://tex.z-dn.net/?f=%5Comega_%7Bf%7D-%5Comega_%7Bi%7D%3D%5Calpha%20t)
Put the value into the formula
![5.0-0=\alpha\times8.0](https://tex.z-dn.net/?f=5.0-0%3D%5Calpha%5Ctimes8.0)
![\alpha=\dfrac{5.0}{8.0}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B5.0%7D%7B8.0%7D)
![\alpha=0.625\ rev/s^2](https://tex.z-dn.net/?f=%5Calpha%3D0.625%5C%20rev%2Fs%5E2)
We need to calculate the angular displacement
Using equation of angular motion
![\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2](https://tex.z-dn.net/?f=%5Ctheta%3D%5Comega_%7Bi%7Dt%2B%5Cdfrac%7B1%7D%7B2%7D%5Calpha%20t%5E2)
Put the value into the formula
![\theta=0+\dfrac{1}{2}\times0.625\times(8.0)^2](https://tex.z-dn.net/?f=%5Ctheta%3D0%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes0.625%5Ctimes%288.0%29%5E2)
![\theta=20\ rev](https://tex.z-dn.net/?f=%5Ctheta%3D20%5C%20rev)
Now, The washer coming to rest from top spin
We need to calculate the angular acceleration
Using equation of angular motion
![\omega_{f}-\omega_{i}=\alpha t](https://tex.z-dn.net/?f=%5Comega_%7Bf%7D-%5Comega_%7Bi%7D%3D%5Calpha%20t)
![\alpha=\dfrac{\omega_{f}-\omega_{i}}{t}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B%5Comega_%7Bf%7D-%5Comega_%7Bi%7D%7D%7Bt%7D)
![\alpha=\dfrac{0-5}{12}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B0-5%7D%7B12%7D)
![\alpha=−0.4167\ rev/s^2](https://tex.z-dn.net/?f=%5Calpha%3D%E2%88%920.4167%5C%20rev%2Fs%5E2)
We need to calculate the angular displacement
Using formula of displacement
![\theta'=\omega_{i}t+\dfrac{1}{2}\alpha t^2](https://tex.z-dn.net/?f=%5Ctheta%27%3D%5Comega_%7Bi%7Dt%2B%5Cdfrac%7B1%7D%7B2%7D%5Calpha%20t%5E2)
Put the value into the formula
![\theta'=5\times12+\dfrac{1}{2}\times(-0.4167)\times12^2](https://tex.z-dn.net/?f=%5Ctheta%27%3D5%5Ctimes12%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%28-0.4167%29%5Ctimes12%5E2)
![\theta'=30\ rev](https://tex.z-dn.net/?f=%5Ctheta%27%3D30%5C%20rev)
We need to calculate the total number of revolution
![\theta''=\theta+\theta'](https://tex.z-dn.net/?f=%5Ctheta%27%27%3D%5Ctheta%2B%5Ctheta%27)
![\theta''=20+30](https://tex.z-dn.net/?f=%5Ctheta%27%27%3D20%2B30)
![\theta''=50\ rev](https://tex.z-dn.net/?f=%5Ctheta%27%27%3D50%5C%20rev)
Hence, The total number of revolution is 50 rev.