Final answer:
Using kinematic equations for rotational motion, the final angular velocity of the grinding wheel, as it coasts to a stop after the circuit breaker trips, was calculated to be 0 rad/s, which is not one of the provided answer choices. There may be an error in the question or the answer choices given.
Step-by-step explanation:
To find the final angular velocity of the grinding wheel, we must first calculate its angular velocity at the time the circuit breaker trips, then use this value to determine how it coasts to a stop.
From the given information, we have an initial angular velocity (ω0) of 20.0 rad/s and a constant angular acceleration (α) of 28.0 rad/s² until time t = 1.60 s.
The angular velocity at the moment the circuit breaker trips (ω1) can be found using the formula for angular velocity under constant acceleration:
ω1 = ω0 + αt
ω1 = 20.0 rad/s + (28.0 rad/s²)(1.60 s) = 20.0 rad/s + 44.8 rad/s = 64.8 rad/s
This is the angular velocity just before it begins to coast. Now, to find the final angular velocity as the grinding wheel coasts to a stop, we can use the final angular velocity formula under constant angular acceleration when the final angular displacement (Θ) is given:
ωf² = ω1² + 2αΘ
Given that the wheel stops (ωf = 0) and it turns through 438 rad while coasting:
0 = 64.8 rad/s² + 2(α)(438 rad)
As the wheel stops, the final velocity squared will be zero, and therefore:
-64.8 rad/s² = 2α(438 rad)
α = -64.8 rad/s² / (2 * 438 rad)
α = -0.074 rad/s²
The negative sign indicates deceleration. Since the angular velocity was 64.8 rad/s before deceleration and it stopped, the final angular velocity is indeed:
0 rad/s
However, none of the provided answer choices are correct. If this was a multiple-choice question, there might be an error in the question or the answer choices provided by the student.