Answer:
14 revolutions
Explanation:
Given that,
Initial angular velocity, [tex]\omega_i=250\ rpm[/tex]
Final angular velocity, [tex]\omega_f=150\ rpm[/tex]
Time, t = 4.2 seconds
We need to find the number of revolutions occur durung this time.
250 rpm = 26.17 rad/s
150 rpm = 15.70 rad/s
Let [tex]\alpha[/tex] is angular acceleration. Using first equation to find it.
[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{15.70 -26.17 }{4.2}\\\\\alpha =-2.49\ rad/s^2[/tex]
Now let us suppose that the number of revolutions are [tex]\theta[/tex].
[tex]\theta=\dfrac{\omega_f^2+\omega_i^2}{2\alpha}\\\\=\dfrac{15.70^2-26.17^2}{2\times -2.49}\\\\=88\ rad[/tex]
or
[tex]\theta=\dfrac{88}{2\pi}\\\\=14\ rev[/tex]
Hence, there are 14 revolutions.
The average speed during the slowdown is 200 RPM.
4.2 seconds is (4.2/60) = 0.07 minute.
(200 rev/minute)x(0.07 minute)= 14 revs
