Final answer:
To calculate the angular acceleration, convert the final angular velocity of 100 rpm to radians per second and use the kinematic equation for angular motion. With the final angular velocity of 10.47 rad/s and time of 5 seconds, the angular acceleration is found to be 2.094 rad/s².
Step-by-step explanation:
The student is asking how to calculate the angular acceleration of a wheel that makes 40.0 revolutions in 5.00 seconds with a final angular velocity of 100 revolutions per minute (rpm) at the end of this period, assuming constant acceleration. To find the angular acceleration, we first need to convert the given final angular velocity to radians per second. Since 1 revolution is 2π radians, and there are 60 seconds in a minute, the final angular velocity is 10.47 rad/s (100 rpm × 2π / 60 s).
We can use the kinematic equation for angular motion, which is ωf = ωi + αt, where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. Since the wheel makes 40 revolutions in 5 seconds and is accelerating uniformly, its initial angular velocity ωi is 0 rad/s. Plugging in the values, we have 10.47 rad/s = 0 rad/s + α(5 s). Solving for α, we find that the angular acceleration is 2.094 rad/s².