Final answer:
The angular speed of the shaft is 71.228 rad/s and the angle through which it has turned is 1126.007 rad.
Step-by-step explanation:
The angular speed and the angle through which the shaft has turned can be calculated using the equations of rotational motion. The angular speed can be calculated using the formula:
ω = ω0 + αt
where ω is the final angular speed, ω0 is the initial angular speed (0 rad/s as the shaft starts from rest), α is the angular acceleration (4.62 rad/s²), and t is the time interval (15.4 s). Plugging in the values, we get:
ω = 0 + (4.62)(15.4) = 71.228 rad/s (a)
The angle through which the shaft has turned can be calculated using the formula:
θ = ω0t + (1/2)αt²
where θ is the angle, ω0 is the initial angular speed, α is the angular acceleration, and t is the time interval. Plugging in the values, we get:
θ = 0 + (1/2)(4.62)(15.4)² = 1126.007 rad (b)