00:01
We'd like to determine the angular velocity of b as a function of time.
00:05
Our speed on any point of our belt is equal to r -a -o -mega -a, equal to r -b -o -b -b.
00:12
So to find our angular acceleration, now we can, omega -b is equal to r -a over rb, which is 0 .10 over .20 times omega -a.
00:26
So that's .5 times omega -a.
00:29
We can differentiate with respect to time to find our angular acceleration, alpha b.
00:35
That's equal to 0 .5 alpha a or 0 .5 times negative 2 .5t, which is negative 2 .5t, radiance per second squared.
00:47
Now, omega b is just equal to the integral of alpha b d t, and so we get negative 0 .625t squared plus some constant c.
00:56
We're given our initial condition for a, and so when we plug that in, we get c is equal to 20 radiance per second.
01:05
So omega -b is negative 0 .625t squared plus 20 radiance per second...