Final answer:
The equation to directly solve for the numerical value of the angular acceleration is α = (Δω / Δt), where Δω is the change in angular velocity and Δt is the change in time. By substituting the given values of the final and initial angular velocities and the time it takes for the turntable to speed up, we can solve for the angular acceleration.
Step-by-step explanation:
The angular acceleration can be found directly from its definition in α = Δω / Δt because the final angular velocity and time are given. We can represent the final angular velocity as 45 rpm and the initial angular velocity as 33 1/3 rpm. Converting both values to rad/s, we have 45 rpm * (2π rad/1 min) = 9π rad/s and 33 1/3 rpm * (2π rad/1 min) = 2π/3 rad/s. The time it takes for the turntable to speed up from 33 1/3 rpm to 45 rpm is given as 5 complete revolutions. Since one revolution is equal to 2π radians, 5 complete revolutions is equal to 10π radians. We can substitute these values into the formula for angular acceleration to solve for the numerical value: α = (9π - 2π/3) / (10π) = 7π/30 rad/s².