You step on the gas pedal in your car, and the car engine’s rotational speed changes from 1200 rpm to 3000 rpm in 3.0 s. What is the engine’s average rotational acceleration?

frequency of engine is given here

initial frequency = 1200 rpm

f_i = 1200/60 = 20 Hz

final frequency = 3000 rpm

f_f = 3000/60 = 50 Hz

now we have angular speed as

$\omega_i = 2\pi f_i$

$\omega_i = 2\pi(20) = 40\pi$

similarly

$\omega_f = 2\pi f_f$

$\omega_f = 2\pi(50) = 100 \pi$

now by the formula of angular acceleration we will have

$\alpha = (\omega_f - \omega_i)/(\Delta t)$

$\alpha = (100\pi - 40\pi)/(3)$

$\alpha = 20\pi rad/s^2$

$\alpha = 62.8 rad/s^2$

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