Answer:
6 s
Explanation:
Let angular acceleration=[tex]\alpha[/tex]
Rotational mass=I
Time,t=2 s
[tex]I'=3 I[/tex]
Angular acceleration,[tex]\alpha=\frac{\tau}{I}[/tex]...(1)
[tex]\alpha'=\frac{\tau}{3I}[/tex]...(2)
Equation(2) divided by equation (1)
[tex]\frac{\alpha'}{\alpha}=\frac{1}{3}[/tex]
[tex]\alpha'=\frac{1}{3}\alpha[/tex]
[tex]\alpha=\frac{\omega-\omega_0}{t}[/tex]
When alpha decreases by 1/3 factor then time increases by 3
The motor needs 2 s originally.If the rotational mass is 3 times the original rotational mass then it takes 3 times the original time.
Time=[tex]2\times 3=6 s[/tex]
Hence, the motor need to bring the blade to its full angular velocity=6 s
