Explanation:
Given that,
Initial angular velocity, [tex]\omega_i=20\ rad/s[/tex]
Final angular velocity, [tex]\omega_f=40\ rad/s[/tex]
Time, t = 5 s
We need to find the total number of revolution made by the wheel during the 5 seconds interval. The first equation of motion gives the acceleration of the wheel as :
[tex]\omega_f=\omega_i+\alpha t\\\\\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{40-20}{5}\\\\\alpha =5\ rad/s^2[/tex]
To find the number of revolution, use third equation of motion as :
[tex]\omega_f^2-\omga_i^2=2\alpha \theta\\\\\theta=\dfrac{\omega_f^2-\omga_i^2}{2\alpha }\\\\\theta=\dfrac{40^2-20^2}{2\times 5}[/tex]
[tex]\theta=120\ rad[/tex]
1 revolution = 6.28 radian
[tex]\theta=19\ rev[/tex]
So, the wheel will make 19 revolution during the 5 seconds interval.
