A fan blade rotates with angular velocity given by ω_z(t) = g - bt², where g = 5.00 rad/s and b = 0.800 rad/s³. Calculate the angular acceleration as a function of time.

The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct³, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s². (b) What is the angular acceleration when θ = π/4 rad?

A fan blade rotates with angular velocity given by ω_z(t) = g - bt², where g = 5.00 rad/s and b = 0.800 rad/s³. Calculate the instantaneous angular acceleration α_z at t = 3.00 s and the average angular acceleration α_av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?

The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt², where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?

The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct³, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s². Find a, b, and c, including their units.