Answer:
Time taken to stop the door is 5 s
Solution:
As per the question:
Angular speed, [tex]\omega = 0.3 rad/s[/tex]
[tex]theta = 90^{\circ}[/tex]
Angular acceleration, [tex]\alpha = 0.06\ rad/s^{2}[/tex]
Now,
Using Kinematic eqn for rotational motion:
[tex]\omega'^{2} = \omega^{2} + 2\alpha \theta[/tex]
[tex]0 = 0.3^{2} + 2\times - 0.06\times \theta [/tex]
[tex]\theta = 0.75\ rad[/tex]
Since, the value of [tex]\theta [/tex] < [tex]\frac{\pi}{2}[/tex], thus we will able to stop the door before it closes.
Time taken to stop the door, t :
[tex]\omega' = \omega + \alpha t[/tex]
[tex]0 = 0.3 - 0.06 t[/tex]
t = 5 s
