Final answer:
The instantaneous angular acceleration (αz) at t = 2.90 s is 0.770 rad/s², as this is a constant value given the conditions of the problem.
Step-by-step explanation:
The question involves calculating the instantaneous angular acceleration (αz) of an object at a specific time given its initial angular velocity (γ) and constant angular acceleration (β). The formula for instantaneous angular acceleration when there is constant acceleration is simply the constant angular acceleration itself.
αz = β
Given that β = 0.770 rad/s³, the instantaneous angular acceleration at any time, including t = 2.90 s, will be αz = 0.770 rad/s².