00:01
So in the first part of this problem, we started from rest at 0 radians per second and ended with a final angular velocity 12 .9 radians per second.
00:12
The time was 3 .06 seconds.
00:19
So to find the average, the constant angular acceleration, which is going to be the same thing as the average when we have constant acceleration, we can use the definition of angular acceleration to be the change in angular velocity over the change in time.
00:34
Now the change is defined as the final minus the initial and the time we start at 0, so we're going to say over time.
00:44
So 12 .9 minus 0 over 3 .06 gives us an angular acceleration of 4 .216 radians per second squared.
00:57
Then to find the angle that we sweep through, we can use kinematics.
01:04
We have acceleration and velocities and we want to find distance.
01:08
So that's the third kinematic equation that's going to be helpful here.
01:10
The final angular velocity squared is equal to the initial angular velocity squared plus 2 times the angular acceleration final minus initial angle.
01:23
Now we can pick our start angle to be 0 and we also know our initial velocity was 0.
01:30
So our angle was final velocity squared over 2 alpha and plugging in 12 .9 squared to 4 .216 gives us an angle swept of 19 .74 radians...