Question

A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700rad/s2. How long does it take to come to rest?

Question 1756: 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. (a) What is the instantaneous angular velocity of the propellers at t=2.0s? (b) What is the angular acceleration?
(a) 45.71 s
(b) 22.86 s
(c) 15.36 s
(d) 8.16 s

Answer 1

The instantaneous angular velocity of the propellers at t = 2.0s is 50.0 rad/s, and the angular acceleration is 25.0 rad/s^2.

Step-by-step explanation:

To find the instantaneous angular velocity of the propellers at t = 2.0s, we can substitute the value of t into the given equation for angular velocity: ω=(25.0t)rad/s. Plugging in t = 2.0s, we can compute ω as follows:

ω=(25.0t)= 25.0(2.0) = 50.0 rad/s.

Therefore, the instantaneous angular velocity of the propellers at t = 2.0s is 50.0 rad/s.

To find the angular acceleration, we can take the derivative of the equation for angular velocity with respect to time. The derivative of ω=(25.0t)rad/s is given by:

α=dω/dt=25.0(rad/s^2).

Therefore, the angular acceleration is 25.0 rad/s^2.