Final answer:
To find the angular displacement of a merry-go-round accelerated from rest to 17.0 rpm in 38 seconds, first convert rpm to rad/s, calculate the angular acceleration, and then use the angular displacement formula resulting in about 34 radians.
Step-by-step explanation:
The student is asking about the calculation of angular displacement of a merry-go-round that accelerates from rest to an angular speed of 17.0 revolutions per minute (rpm) in 38.0 seconds.
To find the angular displacement, we can use the formula for angular displacement under constant angular acceleration, θ = ω0t + 0.5αt2, where θ is the angular displacement, ω0 is the initial angular velocity (which is 0 in this case since it starts from rest), t is the time, and α is the angular acceleration. However, to find α, we first need to convert the final angular speed to radians per second and then use the formula α = (ω - ω0) / t.
First, convert the final angular speed to radians per second: 17.0 rpm × (2π rad/rev) × (1 min/60 s) = 1.78 rad/s. Then, calculate the angular acceleration: α = (1.78 rad/s - 0) / 38.0 s ≈ 0.047 rad/s2. Now, plug these values into the angular displacement formula: θ = 0.5 × 0.047 rad/s2 × (38.0 s)2 ≈ 34 radians.
This gives an angular displacement of approximately 34 radians over the 38 seconds that the child pushes the merry-go-round.