Answer :
Final answer:
To find the angular acceleration of an automobile engine that increases its angular speed from 1200 rev/min to 3000 rev/min in 12 seconds, we calculate the change in angular velocity divided by time, resulting in an angular acceleration of 9000 rev/min².
Explanation:
The student's question involves calculating the angular acceleration of an automobile engine, which is a concept within physics, specifically rotational motion. The formula to find angular acceleration (α) is α = Δω / Δt, where Δω is the change in angular velocity and Δt is the change in time. First, we convert the given angular speeds from revolutions per minute (rev/min) to radians per second (rad/s) using the conversion factor: 1 rev = 2π rad and 1 min = 60 s. Then, we can find the angular acceleration.
To solve the student's question: The engine's angular velocity increases from 1200 rev/min to 3000 rev/min in 12 seconds. To find the angular acceleration in rev/min2, we calculate the change in angular velocity in rev/min and divide it by the time in minutes. The change in angular velocity is 3000 rev/min - 1200 rev/min = 1800 rev/min. Since the change occurs in 12 seconds, or 0.2 minutes, the angular acceleration is 1800 rev/min / 0.2 min = 9000 rev/min².
