 Hello everyone, I am Sachin Rathod working as assistant professor in mechanical engineering department of world change stop technology, Swalapur. Today, we have to see acceleration in mechanism, so the learning outcome of this session is student will able to understand acceleration in mechanism. In last lecture, we have studied how to draw the velocity diagram by relative velocity method. Now, we have to see what is the basic concept behind the acceleration in mechanism for drawing the acceleration in the mechanism, so we are getting the concept in the acceleration in mechanism. So, we have to get the suppose one particle is there that is moving in circular path. Suppose A point is there, this is center point, A point is giving the motions around this circular path, this will give the radius of O A, if it is rotated in the circular path in clockwise direction, so at this instant the velocity of A particle is V, so after some interval of the time, it will take the new position that is the B position, at that point we are getting the new velocity as V plus delta V, that is that will give the change in velocity by an angle of delta theta, so we have to find out the acceleration, so already we have seen the acceleration is nothing but rate of change of velocity with respect to time, so the change of the velocity is obtained from the velocity triangle, so consider this is the O point as a pole, this will give the velocity, this is the velocity V, so after the some interval of time it will take the angle delta theta and the new velocity we are getting V plus delta V in magnitude as well as in the direction, so it will give the velocity of B and it will give the velocity of A, if I join AB it will give change in the velocity, so this change in the velocity is having two component, this one is AC, this one is a CB, so we can draw with the dotted line, this will give the AC one component, this is another component BC, so we can calculate the value of the AC, so why there is a necessary to find out the AC and AB, because we have to find out the acceleration, acceleration is nothing but the rate of change of velocity with respect to time, so AB is giving the change in velocity, so we have to find out the rate of change of velocity with respect to time for getting the acceleration, so this is having the two component, two mutual perpendicular component AC and CB, so AC can calculate AC is equal to OC minus OA, where OC is nothing, it makes an angle delta theta that is makes an angle, so OC is equal to OB cos of delta theta, so OB is equal to V plus delta V cos of delta theta minus OA, OA is nothing but the V, so as limit delta T tends to 0 cos of delta theta is equal to 1, so we are getting V plus delta V minus V, so we are getting is equal to delta V, next component CB, this is a CB component, CB is equal to directly we are getting OB sin of delta theta, because it is a opposite side, therefore OB is equal to V plus delta V sin of delta theta, as delta T tends to 0, we are getting delta theta is equal to V plus delta V delta theta, so the change of the velocity having two mutual component that one first is called as a tangential component of the acceleration, another is called as a normal or radial component of the acceleration, so it is nothing but the tangential component of the acceleration and this one gives the radial component, so AC will gives you the tangential component and CB gives the radial component, radial component means it is moving towards the center, so first one is tangential component of acceleration, it is denoted by the later A T, so A T is equal to tangential component of the acceleration, acceleration is the rate of change of velocity with respect to time, this will gives the rate of change of velocity of one component, this is the rate of change of velocity of another component, so we are getting AC by delta T is equal to AC is equal to delta V, because already we have seen the rate delta T tends to 0, we are getting the value as a delta V, delta V by delta T, so V is equal to r omega, r into omega by omega V, so A T we are getting d omega by d T is equal to angular acceleration, so r into alpha, so we are getting the tangential component A T is equal to r into alpha, so another component that is a normal or radial component it is denoted by the later A n or A r is equal to this one is the radial component it is denoted by the BC, BC divided by delta T, so BC is equal to V plus delta V delta theta by delta T, so we will make the product V delta theta plus delta V delta theta divided by delta T, as rate of change of velocity and delta theta is small component, so we have to negate this term, so we are getting V delta theta by delta T, so delta theta by delta T it is a rate of change of displacement with respect to time, it will gives the V into omega, this is the angular velocity denoted by the later omega, so V into omega is nothing but V is equal to r omega, therefore omega is equal to V by r, so we are getting V square by r, so the tangential component will be the V square by r and the normal tangential component is r omega, so Et is equal to r into alpha and A r is equal to V square by r, this is equation number one, equation number two, so by using these two equation we can easily find out the tangential component and radial component of acceleration and in this we should know the, suppose this is a one link, it is link AB, if it is moving with the angular velocity omega, so it is having the radial component and the tangential component for finding the acceleration, so support is rotated in the clockwise direction, so first one is the radial component, radial component is nothing but we have to draw the parallel line to this AB, suppose this is the A point, we have to draw the parallel line, so along this line the radial component will lie, so suppose the radial component is moving towards the center, so we have to take the V point or the component of this below the A point, so suppose this one is the X point and the value of the radial component is V square by r and next one is the tangential component which is perpendicular to this link, so we have to draw the perpendicular line and the magnitude is equal to tangential component r into alpha make one line, so if I draw in this two point it will gives V point, it is your the radial component, it is a tangential component, this is a basic concept to draw the acceleration, so I have taken these two as a reference, thank you.