DYNAMICS OF A RIGID BODY. 



tance described by the centre parallel to the axis, 

 <f> the angle through which the common normal has turned, and o> 

 the angular velocity of the sphere about that normal, at the end 

 of a tiin.' t. 



l"'ll. A sphere, radius a, is in motion on the surface of a 

 right circular cylinder, radius a + 6, whose axis makes an angle 

 a with the vertical; and is initially in contact with the lowest 

 generator, its centre moving in a direction perpendicular to the 

 axis with such a velocity that the sphere just makes complete 

 revolutions : prove the equations of motion 



do _ dz d$ 

 di - dt 



2 10 



a 



z being the distance described by the centre parallel to the axis, 

 <f> the angle through which the common normal has turned, and ( 

 the angular velocity about that normal, at the end of a time t. 



1542. A rough sphere, radius a, rolls in a spherical bowl of 

 radius a + 6; the centre of the sphere is initially of the same height 

 as the centre of the bowl and is moving hon/.-mtiilly with velocity 

 u : prove that if $ be the angle which the common normal makes 

 the vertical, and <f> the angle through which the vertical 

 plane containing this normal has turned at the end of a time t t 



u 



Also if /?,/", S be the reactions at the point of contact along 

 ommon normal, along the tangent whi.-h lies in the same 

 vertical plane common normal, and at right angles to 



both these directions, 



R.,. stf), r-Sjftol, 5=0; 



