Final answer:
The disk's angular velocity at t=5.0s is calculated using the formula for angular velocity in rotational motion, resulting in 7.0 rad/s given the initial velocity of 2.0 rad/s and angular acceleration of 1.0 rad/s².
Step-by-step explanation:
The question pertains to rotational motion in physics, specifically to calculating the angular velocity of a circular disk that is experiencing a constant angular acceleration. Given the radius of the disk, its initial angular velocity, and a time interval, we need to utilize kinematic equations for rotational motion.
To find the disk's angular velocity at t=5.0s, we use the equation ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity (2.0 rad/s), α is the angular acceleration (1.0 rad/s²), and t is the time (5.0s). Substituting the values, we get ω = 2.0 rad/s + (1.0 rad/s²)(5.0s), which results in an angular velocity of 7.0 rad/s.