[MUSIC] Hello in this video, we are going to get the acceleration of the rigid body. Similarly, maybe it's kind of tricky to obtain it using the absolute coordinate frame. So we are going to use the relative coordinate approach which is the combinations of translation and rotation. Similar to the velocity of the rigid body, when we have a point A and B on the rigid body system, it generally contains a translational and rotational motion. We can split it out the point of a in terms of translational motion of the b and relative velocity with respect to the b. So similar to the velocity case, we are going to split out the acceleration of the A in terms of translational acceleration of the AB and relative acceleration with respect to the B. One thing that is different to pay attention is here, when you want to describe the acceleration of the A with respect to the B as a pure rotation. Usually you have two components which is normal and tangential components or r and theta directional components. Do you remember what was the acceleration for the rigid body polar coordinate? Yes. Tangential will be r theta double dot, or r alpha in the normal vector or the radial vector is a centripetal acceleration which is r omega square. So note that when you work on the acceleration term, there are two components of the relative acceleration which has r theta double dot and r theta dot Square. So similar approaches for the velocity, which is a translational and rotational motion combination, but note that acceleration has two components. Let's work on with example, the similar example that we have worked same example that we have worked on instead here. We are going to obtain our alpha AB and then the acceleration of the A. Since this is kinematics problem, there is no need to draw the free body diagram. And we are going to go over translational and rotational combination methodology. We're with a good point to set the new reference point here to describe the B, yes A which has a here. We have a new reference point x and y and counterclockwise has a positive theta direction. In that case, VB is going to be absolute velocity of the A and relative velocity from the point B with respect to the A. In a similar manner to describe the acceleration of the point B, we are going to obtain the absolute acceleration of the point A and the relative acceleration of point B. So to obtain the translation emotion for the velocity was what the tangential to the rotation, right? But here this is acceleration, what is the acceleration of point A? Yes, it's only centripetal acceleration which is r omega naught square, right? So that's here r omega naught square term which is directed toward the center normal directions. Now the relative acceleration of the point B with respect to the A has generally has two components which is tangential and normal and note that here it's omega ab, the rotational angular acceleration of the a b. Now you have a 2 vector components for the tangential and normal components. And then in the previous example, we obtain those omega A B is same as magnitudes are same as omega naught in the special case. And those are unknowns that what we are supposed to find. So it seems like one equation has two unknowns however, this is vector form, you could split it out X and Y components to solve the equation. Now since B is the point where is guided by a linear of the axis, the vertical axis. So let's use the kinematic constraints saying that the X components of the acceleration, ops here should be the a, acceleration turns out to be 0. So if you have those relationship, which is horizontal components for the acceleration, if you add them up, what you can get is horizontal component of the black arrow part, this one and then the horizontal components of those normal and then tangential and normal acceleration component. So if you sum them up, they should be 0. By solving this equation, you can obtain the unknown alpha and then if you fill up that in back into this equation, you can obtain the unknown A B. Okay, let's graphically check if our approach is correct in a vector direction. You have translational acceleration here, it's not necessarily translation. This is the acceleration of point A and the relative acceleration of point B. If you sum that up, let's see if you can get ops, this doesn't satisfy the kinematic constraints that the acceleration of the B points should be along the axis. Okay, I might gone wrong for the direction for the tangential because the centripetal is always to the center. So I might switch this one down and add them up the vector which ops, doesn't really make any changes, this should be along this axis, what's gone wrong? Maybe not only the direction of the vector, I might have a wrong estimate for the vector magnitude. Therefore if I have a very large tangential acceleration, if you have a vector sum with this to the acceleration of point a, I finally ended up the resultant acceleration of point B along this axis, okay. Okay, that summarizes what we have covered for the acceleration. Pretty much similar step to the velocity except that you are have a relative acceleration which has two components, tangential and normal. Thank you for your attention.
