Comprehension 3 The general motion of a rigid body can be

Last updated: 6/30/2023

Comprehension 3 The general motion of a rigid body can be considered to be a combination of i a motion of its centre of mass about an axis and ii its motion about an instantaneous axis passing through the centre of mass These axes need not be stationary Consider for example a thin uniform disc welded rigidly fixed horizontally at its rim to a massless stick as shown in the figure When the disc stick system is rotated about the origin on a horizontal frictionless plane with angular speed the motion at any instant can be taken as a combination of i a rotation of the centre of mass of the disc about the z axis and ii a rotation of the disc through an instantaneous vertical axis passing through its centre of mass as is seen from the changed orientation of points P and Q Both these motions have the same angular speed in this case 5 P 6 Z I Now consider two similar systems as shown in the figure Case a the disc with its face vertical and parallel to x z plane Case b the disc with its face making an angle of 45 with x y plane and its horizontal diameter parallel to x axis In both the cases the disc is welded at point P and the systems are rotated with constant angular speed about the z axis Q P Z 45 y Case a Case b Which of the following statements about the instantaneous axis passing through the centre of mass is correct 2012 y A It is vertical for both the cases a and b B It is vertical for case a and is at 45 to the x z plane and lies in the plane of the disc for case b C It is horizontal for case a and is at 45 to the x z plane and is normal to the plane of the disc for case b D It is vertical for case a and is 45 to the x z plane and is normal to the plane of the disc for case b B It is for case a and D It is m for h Which of the following statements regarding the angular speed about the instantaneous axis passing through the centre of mass is correct 2012 A It is 200 for both the cases C It is for case a and 2 for case b 0 for case b