Final answer:
The relationship between angular velocity and angle in rotational motion can be expressed as θ(t) = θ₀ + θ˚ * t, assuming a constant angular velocity. for varying angular velocity, the angular position over time is found by integrating θ˚(t) with respect to time.
Step-by-step explanation:
To model the system where the input is the angular velocity (often denoted as θ˚) and the output is the angle (θ) we start with the fundamental relationship that angular . the relationship can be mathematically expressed as θ˚ = dθ/dt. If we integrate both sides of this equation with respect to time, we get θ(t) - θ₀ = ∫ θ˚ dt where θ(t) is the angular position at time t and θ₀ is the initial angle at time t = 0.
Under the assumption of constant angular velocity, the equation simplifies to: θ(t) = θ₀ + θ˚ * t, where θ˚ is the constant angular velocity. If the angular velocity is not constant, the equation integrates θ˚ over time. For a situation with variable angular velocity, you would need to know the exact function of θ˚(t) to perform the integration and determine θ(t).