 Myself, Mr. A. N. Subwade, Assistant Professor, Department of Mechanical Engineering, Walsh and Institute of Technology, Solapur. Today, we are going to study acceleration in a mechanism, learning outcome. At the end of this lecture, student will be able to identify and determine the acceleration of a link. So, consider a rigid link where A and B are the extremities of rigid link AB and this rigid link AB is rotating with angular speed omega radians per second and angular acceleration alpha radians per second square. So, we have to determine the acceleration of B with respect to A. Now, as we know that when a particular particle is moving in a circular path whose velocity changes in magnitude and direction from instant to instant, that particular particle has two components of acceleration. The first component of acceleration is known as centripetal component of acceleration, centripetal or radial component of acceleration which is represented by A of B A in this case. This centripetal component of acceleration of radial component of acceleration will act perpendicular to the velocity given at that instant or it acts parallel to link AB. The second component of acceleration is known as tangential component of acceleration that is represented by A of T B A, tangential component of acceleration of B with respect to A and this tangential component of acceleration acts parallel to the velocity of a particle given at that instant. So, as shown in the diagram, the rigid link AB where this link AB is rotating with angular speed omega radians per second and its angular acceleration is alpha radians per second. So, in previous session, we have discussed about the velocity of a point. So, think here and tell me what is the velocity of B with respect to A? What will be the direction of relative velocity of B with respect to A? Here, velocity of B with respect to A that will be always a perpendicular to the line joining the point A and B and that is shown by V B A. So, this V B A is perpendicular to the link AB and therefore, in order to find out the radial component of acceleration of B with respect to A which is represented by A R of B A that will be equal to square of angular velocity multiplied by link length AB and therefore, omega square into AB. As we know, V is equal to velocity will be product of omega into R and therefore, omega will be equal to V upon R. In our case, V is the velocity of B with respect to A divided by link length AB and therefore, here we can put the angular velocity that is V square B A divided by link length AB square into link length AB and hence, the radial component is given by V square B A divided by link length AB. This is the magnitude by this equation, we can calculate the radial component of acceleration of B with respect to A. Similarly, we can determine the tangential component of acceleration which is represented by A of t B A tangential component of acceleration of B with respect to A and that is equal to angular acceleration of link AB multiplied by link length AB and therefore, this will be equal to alpha into link length AB. So, this is equation number 2 and this equation 2 will give me the tangential component of B with respect to A and now, in order to construct the acceleration diagram, mark any point B dash in space. Now, the acceleration of B with respect to A, it will have two components of acceleration, one is radial and other is tangential. So, radial component of acceleration of B with respect to A is given by V square B A upon link length AB. So, we know the radial component in magnitude and the radial component of acceleration always act perpendicular to the velocity that is perpendicular to V B A or parallel to link AB and that particular radial component will always act towards the centre. So, here point B is rotating with respect to A in anticlockwise direction. So, radial component of B with respect to A will act parallel to AB and towards the centre that is towards point A and hence from point B dash draw a vector parallel to link AB which will represent the radial component of acceleration of B with respect to A. So, draw a vector B dash x, this radial component is parallel to link AB and this will represent the radial component of B with respect to A. Then, tangential component of B with respect to A whose magnitude is alpha AB multiplied by link length AB. So, tangential component of acceleration always act perpendicular to the link AB or parallel to the direction of V B A and hence from point X draw a vector perpendicular to link AB or parallel to velocity of B A in magnitude and direction. So, vector x A dash, this will represent the tangential component of B with respect to A and now join B dash A. So, this vector B dash A what it represents? So, vector B dash A will represent the total acceleration of B with respect to A. So, how to determine the magnitude of total acceleration of B with respect to A? That is acceleration of B with respect to A is equal to sum of radial component and its tangential component. My dear students, please think the radial component and tangential component they are whether they are parallel or perpendicular to each other. So, the radial component and tangential component of B A, they are always a perpendicular to each other and this vector B dash A will represent the total acceleration of link AB or B A. The material is referred from the book of Theory of Machines by Arya Skolmi and S.S. Vatan. Thank you.