00:01
In this question, we have a contraption with a pivot point o, connect with a rod of 120 millimeters long, connected to b here, and that's connected to this rod a, b, that's 180 millimeters long.
00:17
A is attached to a piston that is moving to the right at 2 meters per second, and we want to find the angular velocity of ob.
00:30
So the first thing to do is figure out where the center of rotation is, and there'll be this c over here on the left, which will be we can find by looking at the directions of movement of vb and va.
00:50
We know that this length b .c will be directly in line with ob, which lets us find that this angle right here is 45 degrees then.
01:07
We can then find this angle up here is 30 degrees by knowing that ac into that velocity vector is a right angle.
01:23
And then this final angle here, because all of the angles in triangle, if that add up to 180 degrees, this angle must be 105 degrees.
01:33
So we have all of our necessary angles now.
01:36
After we have the necessary angles, we can, can find some lengths that we will need.
01:44
So we know ab, we now need to find ac and then bc.
01:56
So we can use the law of signs for this, the sign of 105 degrees divided by length ab should equal the sign of 30 degrees over length bc, which if we put all of all of our value, in and put this into our calculator, we get that b .c equals 93 .2 millimeters.
02:31
We can then do the same thing to find ac, so sign of 105 over a, b equals the sign of 45 degrees now over ac, which again doing the algebra, leaves us with ac equals 131 .1 .1.
02:55
8 millimeters...