Final answer:
The final angular velocity of a wheel, starting from rest and undergoing a constant angular acceleration of 5.0 rad/s² through 300 rad, is 10.0 rad/s.
Step-by-step explanation:
Calculating Final Angular Velocity
To find the final angular velocity of a wheel with constant angular acceleration, we can use the kinematic equations for rotational motion. Given that the angular acceleration is 5.0 rad/s² and the wheel starts from rest, the equation ω² = ω_0² + 2αΘ relates the final angular velocity (ω), the initial angular velocity (ω_0), the angular acceleration (α), and the angle turned through (Θ). Since the wheel starts from rest, the initial angular velocity ω_0 is 0. The angle turned through, Θ, is 300 rad. Substituting these values into the equation:
ω² = 0 + 2(5.0 rad/s²)(300 rad)
By solving for ω, we find that the final angular velocity is 10.0 rad/s.