The angular speed of an automobile is increased uniformly from 1500 rev/min to 2500 rev/min in 12 seconds. Calculate the angular acceleration

Sure, here's how to calculate the angular acceleration:

Step 1: Convert the angular speeds from revolutions per minute to radians per second.

We know that 1 revolution is equal to 2π radians and 1 minute is equal to 60 seconds.

So, the initial angular speed (ωi) is 1500 rev/min * 2π rad/rev * 1 min/60 sec = 157.08 rad/sec.

The final angular speed (ωf) is 2500 rev/min * 2π rad/rev * 1 min/60 sec = 261.8 rad/sec.

Step 2: Use the formula for angular acceleration, which is (ωf - ωi) / t, where t is the time in seconds.

So, the angular acceleration (α) is (261.8 rad/sec - 157.08 rad/sec) / 12 sec = 8.73 rad/sec².

Therefore, the angular acceleration of the automobile is 8.73 rad/sec².