Final answer:
The angular acceleration of the drill is 1010 rad/s². The drill rotates through an angle of 1562.08 rad during this period.
Step-by-step explanation:
To find the angular acceleration, we need to convert the speed from rev/min to rad/s. Since 1 rev = 2π rad, the angular speed is calculated as: 2.70 x 10⁴ rev/min x 2π rad/rev x 1 min/60 s = 2827 rad/s. The angular acceleration can be found using the formula: ωf = ωi + αt, where ωi is the initial angular velocity, ωf is the final angular velocity, α is the angular acceleration, and t is the time. Rearranging the formula, we have: α = (ωf - ωi) / t. Substituting the given values, we get: α = (2827 rad/s - 0 rad/s) / 2.80 s = 1010 rad/s².
To determine the angle through which the drill rotates during this period, we can use the formula: θ = ωi t + (1/2) α t², where θ is the angle, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. Substituting the given values, we have: θ = 0 rad/s x 2.80 s + (1/2) (1010 rad/s²) (2.80 s)² = 1562.08 rad.