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estimate how large the spin n of a pencil would have to be for it to be stable in the vertically upright position
the sleeping top by performing a perturbation analysis show that a top will be stable in the vertically upright
investigate the steady precession of a top for the case in which the axis of the top moves in the horizontal plane
ball rolling on a rotating turntable a rough horizontal turntable is made to rotate about a fixed vertical axis through
ball rolling on a slope a uniform ball can roll or skid on a rough plane inclined at an angle beta to the
determine the dynamical symmetry if any of each the following bodies about their centres of massi a frisbeeii a piece
a uniform rectangular block has mass m and sides 2a 2b and 2c find the principal moments of inertia of the block i at
find the principal moments of inertia of a uniform cube of mass m and side 2a i at its centre of mass ii at the centre
a uniform hemisphere has mass m and radius a a spinning top is made by fitting the hemisphere with a light spindle ab
a uniform circular disk has mass m and radius a a spinning top is made by fitting the disk with a light spindle ab
1 find the principal moments of inertia of a uniform circular disk of mass m and radius a i at its centre of mass and
in crystalline materials the ordinary elastic moduli are replaced by cijkl a fourth order tensor with eighty one
if the matrix t represents a second order tensor show that det t is an invariantwe have now found three invariant
1 write out the transformation formula for a fifth order tensor the main difficulty is finding enough suffix names2
if a mass of liquid in gravity free space is in equilibrium then it has the form of a sphere stabilised by its own
a sealed circular can of radius a is three-quarters full of water of density rho the remainder being air at pressure p0
newtons bucket a bucket half full of water is made to rotate with angular speed about its axis of symmetry which is
a horizontal turntable is made to rotate about a fixed vertical axis with constant angular speed a hollow uniform
one end of a straight rod is fixed at a point o on a smooth horizontal table and the rod is made to rotate around o
consider given problem again this time find the motion of the particle by using the transformed energy equationproblem
larmor precession a particle of mass m and charge e moves in the force field fr and the uniform magnetic field bk where
a particle p of mass m can slide along a smooth rigid straight wire the wire has one of its points fixed at the origin
a circular cone with semi-angle alpha is fixed with its axis of symmetry vertical and its vertex o upwards a second
use the velocity and acceleration transformation formulae to derive the standard expressions for the velocity and
two hollow spheres have radii a and b b gt a and their common centre o is fixed a rigid ball of radius 1 2 b - a can