The average angular acceleration of the fan is
[tex]\alpha_{\rm avg}=\dfrac{\Delta\omega}{\Delta t}=\dfrac{200\frac{\rm rev}{\rm min}-1000\frac{\rm rev}{\rm min}}{2\,\rm s}=-6.67\dfrac{\rm rev}{\mathrm s^2}[/tex]
The number of revolutions after time [tex]t[/tex] is given by
[tex]\theta=\omega_0t+\dfrac{\alpha}2t^2[/tex]
Acceleration is assumed to be constant, so [tex]\alpha=\alpha_{\rm avg}[/tex] and over the 2 second interval we have
[tex]\theta=\left(1000\dfrac{\rm rev}{\rm min}\right)(2\mathrm s)+\dfrac{\alpha_{\rm avg}}2(2\,\mathrm s)^2=20\,\mathrm{rev}[/tex]
so the answer is A.
No of revolution is defined as the no of loops taken from the starting to the end to the end from the same point started. The number of the revolution blade experiences will be 20.
Angular acceleration is defined as the pace of change of angular velocity with reference to time.
[tex]\rm{\alpha _{avg}= \frac{w_f-w_i}{t_f-t_i}}[/tex]
given ,
initial angular velocity = 1000 rev/min = 16.67 rev /sec
final angular velocity = 200 rev/min = 3.33 rev/sec
time taken = 2 second
[tex]\rm{\alpha _{avg}= \frac{w_f-w_i}{t_f-t_i}}\\\\\\\rm{\alpha _{avg}= \frac{3.33-16.67}{0.3}}\\\\\\\rm{\alpha _{avg}= -6.67 rev/ sec^2[/tex]
According to newtons second law of motion,
No of revolution after time t
[tex]\rm{\theta= \omega_it+\frac{1}{2} \alpha t^{2} }\\\\\\\rm{\theta= \ 16.67\times2+\frac{1}{2}(-6.67)\times{2}^{2} }\\\\\\\rm{\theta= \ 16.67\times2-\frac{1}{2} (6.67)\times{2}^{2} }\\\\\\\rm{\theta= \ 16.67\times2-\frac{1}{2} (6.67)\times{2}^{2} }\\\\\\\rm{\theta= \ 33.3- 13.3}\\\\\\\rm{\theta= \ 20rev }\\\\\\[/tex]
Therefore the number of revolutions the blade undergoes will be 20 revolutions.
To know more about angular acceleration refer to the link ;
https://brainly.com/question/408236
