To find the angular acceleration, we first need to convert the final angular velocity from rotations per minute to radians per second.
1 revolution = 2π radians
20,000 rotations per minute = (20,000 rotations/minute) * (2π radians/rotation) * (1 minute/60 seconds) = (20,000 * 2π) / 60 radians/second ≈ 2094.4 radians/second
Next, we need to convert the time from minutes to seconds:
5 minutes = 5 minutes * 60 seconds/minute = 300 seconds
Now, we can calculate the angular acceleration using the formula:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Since the object is starting from rest, the initial angular velocity is 0 radians/second.
Angular acceleration (α) = (2094.4 radians/second - 0 radians/second) / 300 seconds = 2094.4 radians/second / 300 seconds ≈ 6.98 radians/second²
Therefore, the angular acceleration of the object is approximately 6.98 radians/second².