Chapter 6 Plane Kinematics of Rigid Bodies Rigid body: A body (system) is so rigid such that the relative positions of all the mass elements do not change during motion.

= angular velocity = angular acceleration q (angular displacement) 

Velocity of a point P relative to another point O with a fixed distance from P (could be a fixed point in a rigid body. Direction defined by Right Hand Rule. P

Acceleration of a point P relative to another point O with a fixed distance from P. Exercise Prove that the above statement is identical to:

Relative motion of two points of a fixed separation (i. e Relative motion of two points of a fixed separation (i.e. on a rigid plane): Example : Draw a vector diagram to show the relation between

Instantaneous Centre of zero velocity Draw two lines perpendicular to the velocities of points A and B of a rigid body. Their intercept is an instantaneous stationary point (zero velocity).

Relative acceleration is:

Let s = 00’ = r  Example : For pure rolling without slipping, derive y x Let s = 00’ = r  (c) For the new position C' from C : x = s - rsin and y = r - rcos when  = 0, vc = 0 (d) when  = 0,

Example A wheel has a radius R = 0.3 m. Point P is 0.2 m from the centre O, which is moving with vo = 3 m/s. Find . Solution:

Example : The structure has the following dimensions: rB/A = 0.1 m, rC/D = 0.075 m, h = 0.05 m, X = 0.25 m. CD = 2 rad/s. Find : AB , BC h D X A B C x y