Question

on takeoff, the propellers on a uav (unmanned aerial vehicle) increase their angular velocity from rest at a rate of ω = (25.0t) rad/s for 3.0 s. (a) what is the instantaneous angular velocity of the propellers at t = 2.0 s? (b) what is the angular acceleration?​

Answer 1

Hi there!

a)
We can find the angular velocity at t = 2.0 s by plugging in this value into the equation.

$\omega (t) = 25.0t \\\\\omega (2) = 25.0(2) = \boxed{50.0 \frac{rad}{s}}$

b)

The angular acceleration is the derivative of the angular velocity, so:
$\alpha (t) = \frac{d\omega}{dt} (25.0t) = 25.0$

Thus, the angular acceleration is a constant 25 rad/s².