Final answer:
The angular velocity of the carnival ride at 6.3 rad with an angular acceleration of 2.0 rad/s² is found to be 5.0 rad/s using the kinematic equations for rotational motion.
Step-by-step explanation:
The question relates to a scenario where a carnival ride experiences angular acceleration and we want to find its angular velocity at a certain angle. To solve this physics problem, we can use one of the kinematic equations adapted for rotational motion, specifically the equation ω² = ω₀² + 2αθ, where ω is the final angular velocity, ω₀ is the initial angular velocity (in this case 0 rad/s because it starts from rest), α is the angular acceleration, and θ is the angle in radians through which the ride has rotated.
Plugging in the values:
- α = 2.0 rad/s²
- θ = 6.3 rad
We calculate:
ω² = 0 + 2(2.0 rad/s²)(6.3 rad) = 25.2 rad²/s²
So, ω = √(25.2 rad²/s²) = 5.0 rad/s
Therefore, the angular velocity at 6.3 rad is 5.0 rad/s.