Answer:
(I). The angular acceleration and number of revolution are -2.5 rad/s² and 500 rad.
(II). The torque is 84.87 N-m.
Explanation:
Given that,
Initial spinning = 50.0 rad/s
Time = 20.0
Distance = 2.5 m
Mass of pole = 4 kg
Angle = 60°
We need to calculate the angular acceleration
Using formula of angular velocity
![\omega=-\alpha t](https://tex.z-dn.net/?f=%5Comega%3D-%5Calpha%20t)
![\alpha=-\dfrac{\omega}{t}](https://tex.z-dn.net/?f=%5Calpha%3D-%5Cdfrac%7B%5Comega%7D%7Bt%7D)
![\alpha=-\dfrac{50.0}{20.0}](https://tex.z-dn.net/?f=%5Calpha%3D-%5Cdfrac%7B50.0%7D%7B20.0%7D)
![\alpha=-2.5\ rad/s^2](https://tex.z-dn.net/?f=%5Calpha%3D-2.5%5C%20rad%2Fs%5E2)
The angular acceleration is -2.5 rad/s²
We need to calculate the number of revolution
Using angular equation of motion
![\theta=\omega_{0}t+\dfrac{1}{2}\alpha t](https://tex.z-dn.net/?f=%5Ctheta%3D%5Comega_%7B0%7Dt%2B%5Cdfrac%7B1%7D%7B2%7D%5Calpha%20t)
Put the value into the formula
![\theta=50\times20-\dfrac{1}{2}\times2.5\times20^2](https://tex.z-dn.net/?f=%5Ctheta%3D50%5Ctimes20-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes2.5%5Ctimes20%5E2)
![\theta=500\ rad](https://tex.z-dn.net/?f=%5Ctheta%3D500%5C%20rad)
The number of revolution is 500 rad.
(II). We need to calculate the torque
Using formula of torque
![\vec{\tau}=\vec{r}\times\vec{f}](https://tex.z-dn.net/?f=%5Cvec%7B%5Ctau%7D%3D%5Cvec%7Br%7D%5Ctimes%5Cvec%7Bf%7D)
![\tau=r\times f\sin\theta](https://tex.z-dn.net/?f=%5Ctau%3Dr%5Ctimes%20f%5Csin%5Ctheta)
Put the value into the formula
![\tau=2.5\times4\times 9.8\sin60](https://tex.z-dn.net/?f=%5Ctau%3D2.5%5Ctimes4%5Ctimes%209.8%5Csin60)
![\tau=84.87\ N-m](https://tex.z-dn.net/?f=%5Ctau%3D84.87%5C%20N-m)
Hence, (I). The angular acceleration and number of revolution are -2.5 rad/s² and 500 rad.
(II). The torque is 84.87 N-m.