Page 2 : (c) Constratned = Mohon . ., Note:- whenever one finds ‘the, , (2) STRING Cons TeaiInT fumber of eyrs < No- of UNknows, , (b) Weohe (ongtRainT b, , Must think of Constraint Laanon, What Is A Constrained Motion?, , aaa, , In other words, Constrained motion results when an object is forced to move in a restricted way., , For example, OBJECT may have to move along a curved track, slide on a table that may accelerate upwards, stay in, contact with an accelerating wedge, etc., , e Types of Constrained Motion:, There are three types of Constrained Motion:, , 1. Completely constrained, 2. Partially or Successfully constrained motion and, 3. Incompletely constrained motion, , 1. Completely constrained, , When the motion between a pair is limited to a definite direction irrespective of the direction of force applied,, then the motion is said to be a completely constrained motion.

Page 3 : Example of Completely constrained motions:, ¢ The motion of a square bar in a square hole, , 2. Partially constrained, , Partially or successfully constrained motion can have motion in more than one direction without any external, forces. But when external forces are applied it can have motion only in one direction., , 3. Incompletely Constrained Motion:, , When the motion between a pair can take place in more than one direction. It is said to be incompletely, constrained motions., , A change in the direction of the affected force can change the direction of relative motion between the pair., , Types of Motions, , Completely Constrained Incompletely Constrained Successfully Constrained, Motion Motion Motion

Page 4 : When two objects are connected through a string and if the string have the following properties:, (a) the length of the string remains constant I.e. inextensible string, , (b) always remains tight, does not slacks, , Then the parameters of the motion of the objects along the length of the string and in the direction of extension have a, , definite relation between them:, , Steps for string constraint, , Step 1: identify all the objects and number of strings in the problem., Step 2: assume variable to represent the parameters such as displacement, velocity, acceleration etc., , 1. Object which moves along a line can be specified by one variable., 2. Object moving in a plane are specified by two variables., 3. Objects moving in 3D requires three variables to represent the motion., , Step 3: identify a single string and divide it into different linear sections and the equations in a format., , Ly+ 0. + , fil» + It nts th, 2 4, , STEP 4: differentiate w.r.t time, , dt, =» dh. ek. + — =: O, dt dr dt, , AQ. yate of