The angular speed of an automobile is increased uniformly from 1000 rev/min to 2000 rev/min in 12 seconds. Calculate the angular acceleration.*1 point8.73 rads^-210.27 rads^-212.27 rads^-214.71 rads^-2

To solve this problem, we first need to convert the angular speeds from revolutions per minute to radians per second, since the standard unit of angular speed in physics is radian per second (rad/s).

1 revolution is equal to 2π radians, and 1 minute is equal to 60 seconds.

So,

Initial angular speed (ω1) = 1000 rev/min * (2π rad/1 rev) * (1 min/60 s) = 104.72 rad/s

Final angular speed (ω2) = 2000 rev/min * (2π rad/1 rev) * (1 min/60 s) = 209.44 rad/s

The formula for angular acceleration (α) is change in angular speed divided by change in time.

So,

α = (ω2 - ω1) / t

Substituting the given values,

α = (209.44 rad/s - 104.72 rad/s) / 12 s = 8.73 rad/s²

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

To solve this problem, we first need to convert the angular speeds from revolutions per minute to radians per second because the standard unit of angular speed in physics is radian/second.

1 revolution = 2π radians 1 minute = 60 seconds

So,

Initial angular speed (ω1) = 1000 rev/min * 2π rad/rev * 1 min/60 sec = 104.72 rad/sec

Final angular speed (ω2) = 2000 rev/min * 2π rad/rev * 1 min/60 sec = 209.44 rad/sec

Angular acceleration (α) is the rate of change of angular speed. It can be calculated using the formula:

α = (ω2 - ω1) / t

where ω1 = initial angular speed, ω2 = final angular speed, t = time.

Substituting the given values into the formula, we get:

α = (209.44 rad/sec - 104.72 rad/sec) / 12 sec = 8.73 rad/sec²

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