Final answer:
The equation for angular acceleration as a function of time, for constant angular acceleration, is represented simply by α(t) = a, where a is the constant angular acceleration.
Step-by-step explanation:
To determine the equation for angular acceleration as a function of time, α(t), we need to consider the given information. Angular acceleration is defined as the change in angular velocity with respect to time. The problem suggests we are dealing with constant angular acceleration, which can be encoded using the variables a, b, and c in place of numerical values.
The general form of the angular velocity as a function of time can be expressed as ω(t) = at + b, where a is the constant angular acceleration, and b is the initial angular velocity. By differentiating ω(t) with respect to time, we find that α(t) = da/dt. Since a is constant, the derivative results in simply α(t) = a.
Therefore, the equation for the angular acceleration as a function of time, for constant angular acceleration, is:
α(t) = a