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 are the steps to calculate the angular acceleration:

1. First, we need to convert the angular speeds from revolutions per minute to radians per second because the standard unit of angular speed is rad/s. We know that 1 rev = 2π rad and 1 min = 60 s. So, we have:

   Initial angular speed (ωi) = 1500 rev/min * 2π rad/rev * 1 min/60 s = 157 rad/s Final angular speed (ωf) = 2500 rev/min * 2π rad/rev * 1 min/60 s = 261.8 rad/s

2. The formula for angular acceleration (α) is change in angular speed divided by the change in time. Mathematically, it is represented as α = (ωf - ωi) / t.

3. Substituting the given values into the formula, we get:

   α = (261.8 rad/s - 157 rad/s) / 12 s = 8.73 rad/s²

So, the angular acceleration of the automobile is 8.73 rad/s².