00:01
Hi everyone.
00:01
So what we have here is a ball of mass m that is moving along a circular path that's given by r is equal to 2 times rz coast theta.
00:11
We know the arm has a constant angular velocity, theta dot equal to theta dot not.
00:16
And since we know it's constant, we also know that theta double dot is equal to zero.
00:21
Or what we're asked to solve for is the angle of theta, which is less than 45 degrees when the ball leaves the surface.
00:28
The way we're going to do this is use and apply our knowledge of normal tangential and rotational motion and combine that with free body diagrams and develop equations of motion using newton's second law, namely f equals ma, to solve this problem and solve this theta.
00:45
So let's go ahead and get started.
00:47
We know that r is equal to 2 rc coast theta, therefore r dot will then be equal to negative 2 rc sine theta times theta dot.
00:59
And we know that our double dot, will then be equal to negative 2rc, close theta times theta dot squared, minus 2rc sine theta times theta double dot.
01:13
Since we know that theta dot is constant and theta double dot is zero, what we can do is we can go ahead and solve for our accelerators from the r direction.
01:23
We know that a r is equal to r double dot minus r theta dot squared.
01:28
What this gives us is an a r that's equal to negative 4...