Final answer:
The final angular velocity after the switch is flipped is approximately 8.18 rad/s. The turntable makes approximately 18.85 revolutions during the acceleration. The angular acceleration of the turntable is approximately 0.11 rad/s². The total time taken for the turntable to reach 78 rpm is approximately 41.78 seconds.
Step-by-step explanation:
a) To determine the final angular velocity after the switch is flipped, we need to calculate the change in angular velocity. The initial angular velocity is 33 1/3 rpm and the final angular velocity is 78 rpm. We can convert these values to radians per second by multiplying by 2π/60. The initial angular velocity is approximately 3.49 rad/s and the final angular velocity is approximately 8.18 rad/s.
b) To find the number of revolutions the turntable makes during the acceleration, we can use the formula Δθ = ωi * t + 1/2 * α * t^2, where Δθ is the change in angle, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. Since the final angular velocity is known, we can solve for t. Substituting the values, we find that the turntable makes approximately 18.85 revolutions during the acceleration.
c) The angular acceleration of the turntable can be found using the formula α = (ωf - ωi) / t, where ωi is the initial angular velocity, ωf is the final angular velocity, and t is the time. Substituting the values, we find that the angular acceleration is approximately 0.11 rad/s².
d) The total time taken for the turntable to reach 78 rpm can be found using the equation ωf = ωi + α * t, where ωi is the initial angular velocity, α is the angular acceleration, ωf is the final angular velocity, and t is the time. Rearranging the equation to solve for t, we find that the total time taken is approximately 41.78 seconds.