Final answer:
To find the number of revolutions a bicycle wheel made after accelerating from rest for 11 seconds with an angular acceleration of 4.5 rad/s², we used rotational motion equations to calculate the angular displacement and then divided by 2π to convert to revolutions, resulting in approximately 43.36 revolutions.
Step-by-step explanation:
To calculate how many revolutions the bicycle wheel made, we need to use equations for rotational motion. The given values are the initial angular velocity (ω0 = 0 rad/s, since it starts from rest), the angular acceleration (alpha = 4.5 rad/s²), and the time interval (t = 11 s).
The equation for the angular displacement (theta) in radians after a time t under constant angular acceleration is:
theta = ω0t + 0.5*alpha*t²
Plugging in the given values:
theta = (0 rad/s)(11 s) + 0.5*(4.5 rad/s²)(11 s)²
theta = 0 + 0.5*4.5*121
theta = 272.25 rad
Since one revolution is 2π radians, we divide the angular displacement by 2π to get the number of revolutions (N):
N = theta / (2π)
N = 272.25 rad / (2π)
N = 43.36 revolutions
The bicycle wheel made approximately 43.36 revolutions during the 11 seconds it was accelerating.