Respuesta :
Answer:
194.81 revolutions
Explanation:
Given that,
Initial angular velocity, [tex]\omega_i=3700\ rpm[/tex]
Final angular velocity, [tex]\omega_f=1800\ rpm[/tex]
Time, t = 4.25 seconds
We need to find the number of revolutions occur during this time.
3700 rpm = 387.46 rad/s
1800 rpm = 188.49 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{188.49 -387.463 }{4.25}\\\\\alpha =-46.81\ 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{188.49 ^2-387.463 ^2}{2\times -46.81}\\\\=1224.087\ rad[/tex]
or
[tex]\theta=\dfrac{1224.087}{2\pi}\\\\=194.81\ rev[/tex]
Hence, there are 194.81 revolutions.
