Question

A turbine blade rotates with angular velocityν(t)=2.00 rad/s⁻².1.00 rad/s³t². what is the angular acceleration of the blade at t=9.10s?

Answer 1

The angular acceleration of the turbine blade at t = 9.10 s is -18.20 rad/s³, which represents a decelerating motion.

Step-by-step explanation:

To find the angular acceleration of the turbine blade at a specific time, we can differentiate the given angular velocity equation ν(t) with respect to time t.

The question provides the angular velocity ν(t) as 2.00 rad/s⁻² ± 1.00 rad/s³t².

Therefore, angular acceleration α(t) is the derivative of ν(t) with respect to t.

The given angular velocity function is:

ν(t) = 2.00 - 1.00t²

To get angular acceleration, we differentiate:

α(t) = dν(t)/dt = -2.00·t

Now substitute t = 9.10 s into the equation for α(t):

α(9.10) = -2(9.10) rad/s³
α(9.10) = -18.20 rad/s³

The angular acceleration of the turbine blade at t = 9.10 s is α(9.10) = -18.20 rad/s³, indicating that the turbine is decelerating.