Final answer:
To find the angular displacement of a merry-go-round when a child pushes it to an angular speed of 15 rpm in 43 seconds, we use the formula θ = ωt / 2 and convert the time to minutes.
Step-by-step explanation:
The student is asking about the concept of angular displacement, which is a measure of how far a rotating object has turned during its motion. The angular displacement can be calculated if the angular acceleration is constant, starting from rest, and if we know the final angular speed and the time taken to reach that speed. The formula to use is θ = ωt / 2, where θ is the angular displacement in revolutions, ω is the angular speed in revolutions per minute (rpm), and t is the time in minutes. However, because the time is given in seconds, we first need to convert it to minutes by dividing by 60. Using the final angular speed of 15 rpm and the time of 43 s, and applying the formula, we calculate the angular displacement during the 43-second interval.