To find the angular acceleration of an object, we need to convert the given rotational speed from RPM (rotations per minute) to radians per second.
First, let's convert 20,000 RPM to radians per second: 1 rotation = 2π radians 1 minute = 60 seconds
So, to convert RPM to radians per second, we can use the following conversion factor: 20,000 RPM * (2π radians / 1 rotation) * (1 rotation / 60 seconds) = 20,000 * 2π / 60 radians per second
Simplifying further: 20,000 * 2π / 60 radians per second ≈ 2094.4 radians per second
Now, we can use the equation for angular acceleration:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given: Initial angular velocity (ω1) = 0 (since the object is accelerated from rest) Final angular velocity (ω2) = 2094.4 radians per second Time (t) = 5 minutes = 5 * 60 seconds = 300 seconds
Using the equation:
Angular acceleration (α) = (2094.4 - 0) / 300 radians per second squared
Simplifying:
Angular acceleration (α) ≈ 6.98 radians per second squared
Therefore, the angular acceleration of the object is approximately 6.98 radians per second squared.