Answer :
Final answer:
The wheel with an initial angular velocity of 2.00 rad/s and an angular acceleration of 5.0 rad/s² has rotated through an angle of 270 radians after 10 seconds.
Explanation:
Calculating Angular Displacement
We need to calculate the angular displacement (θ) of a wheel that starts with an initial angular velocity (ω0) of 2.00 rad/s and has a constant angular acceleration (α) of 5.0 rad/s² over a time (t) of 10 s. Using the formula for angular displacement θ = ω0t + 0.5αt², we can plug in the given values:
θ = (2.00 rad/s × 10 s) + 0.5 × (5.0 rad/s² × (10 s)²) = 20 rad + 0.5 × 5.0 rad/s² × 100 s² = 20 rad + 250 rad = 270 rad.
Angular Displacement and Rotation
Thus, the wheel has rotated through an angle of 270 radians in the 10-second interval.
