Difficulty With Wording of a Problem

[verd]

Hi. So, I don't quite understand EXACTLY what they're asking me here.
Problem statement:


A fan blade rotates with angular velocity given by $$\omega _{z}(t) = ( 5.10 rad/s) - ( 0.785 rad/s^3) t^{2}$$

a.) Calculate the angular acceleration as a function of time.


Alright, I understand the kinematic formulas for constant angular acceleration... But are they asking me for an instantaneous angular acceleration? ...I wouldn't know about how to go about that, being that I would need to take the derivative of the function but with respect to angular displacement...

What exactly are they looking for by saying, "angular acceleration"? Any suggestions as to how to begin?



Thanks, by the way.

 

[whozum]

Angular acceleration is the time derivative of angular velocity.

 

[thepatientmental]

Hi there,

I can understand why you may be having difficulty understanding the wording of this problem. It seems like the problem statement is asking you to calculate the angular acceleration of a rotating fan blade, which is represented by the given function. In this case, the angular acceleration is not instantaneous, but rather a function of time.

To begin, you can use the formula for angular acceleration, which is given by α = dω/dt, where ω is the angular velocity and t is time. In this case, you will need to take the derivative of the given function with respect to time. This will give you the angular acceleration as a function of time.

I hope this clarifies the problem statement for you and helps you to begin solving it. If you have any further questions, do not hesitate to ask. Good luck!