Question

On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity for 3.0 s from rest at a rate of ω=(25.0t) rad/s where t is measured in seconds. What is the instantaneous angular velocity of the propellers at t=2.0s? What is the angular acceleration?

a) 50.0 rad/s
b) 25.0 rad/s²
c) 75.0 rad/s
d) 50.0 rad/s²

Answer 1

At t = 2.0 s, the instantaneous angular velocity of the propellers is 50.0 rad/s. The angular acceleration is 25.0 rad/s².

Step-by-step explanation:

The angular velocity of a propeller at a given time can be found by integrating the angular acceleration equation. In this case, the angular acceleration is given by ω = 25.0t rad/s, where t is measured in seconds. To find the instantaneous angular velocity at t = 2.0 s, we can substitute this value into the equation.

ω = 25.0(2.0) = 50.0 rad/s

The angular acceleration can be found by taking the derivative of the angular velocity equation. In this case, the derivative is the rate of change of ω with respect to time. Since the given equation is linear in t, the derivative is constant.

ω' = 25.0 rad/s²