Final answer:
To calculate the angular velocity of the wheel after 10 seconds, we use the kinematic equation ω = ω_0 + αt, which gives us an angular velocity of 22.0 rad/s.
Therefore, the angular velocity of the wheel after 10 seconds is 22.0 rad/s.
Step-by-step explanation:
The question involves calculating the angular velocity of a wheel after a certain time period given its initial angular velocity and a constant angular acceleration rate. Given that the wheel's initial angular velocity is 2.0 rad/s, and considering a constant angular acceleration of 2.0 rad/s² (as implied by the provided context of related problems that show angular accelerations), we can use the kinematic equation ω = ω_0 + αt to find the angular velocity after a specific time.
In this case, after 10 seconds (ω_0 = 2.0 rad/s, α = 2.0 rad/s², t = 10 s), we get:
ω = 2.0 rad/s + (2.0 rad/s²)(10 s)
ω = 2.0 rad/s + 20.0 rad/s
ω = 22.0 rad/s
Therefore, the angular velocity of the wheel after 10 seconds is 22.0 rad/s.