Answer:
67 revolutions
Explanation:
t = Time taken
[tex]\omega_f[/tex] = Final angular velocity
[tex]\omega_i[/tex] = Initial angular velocity
[tex]\alpha[/tex] = Angular acceleration
[tex]\theta[/tex] = Number of rotation
Equation of rotational motion
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\frac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\frac{7-0}{7}\\\Rightarrow a=1\ rev/s^2[/tex]
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2}{2\alpha}\\\Rightarrow \theta=\frac{7^2-0^2}{2\times 1}\\\Rightarrow \theta=24.5\ rev[/tex]
Number of revolutions in the 7 seconds is 24.5
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\frac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\frac{0-7}{12}\\\Rightarrow a=-0.583\ rev/s^2[/tex]
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2}{2\alpha}\\\Rightarrow \theta=\frac{0^2-7^2}{2\times -0.583}\\\Rightarrow \theta=42.02\ rev[/tex]
Number of revolutions in the 12 seconds is 42.02
Total total number of revolutions in the 20 second interval is 24.5+42.02 = 66.52 = 67 revolutions
