Question

hi

can u help me,please
my question is about the equilibrium:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity BELOW its
geometrical center, is:
A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. not in equilibrium
E. none of the above

the answer is A !!
how it come ??!!

Answer 1

When the centre of gravity lies above the geometrical centre,the torque due to weight about the point of contact rotates the cylinder furthur in the direction of the displacement of the geometrical centre,

However when the center of gravity lies below the geometrical center, the torque tends to rotate the cylinder back to its initial position i.e. in the direction opposite to the motion of the geometrical center.
Hence the first case corresponds to the unstable eqbm and the second one to the stable one.
You can either imagine the direction of torques by forming a mental picture or you can sketch the figures and then see. You will easily note what i am trying to say.

The entire difference is made by the fact that the points below the geometrical center move in the direction opposite to that of the motion of the geometrical center and those above it move in its direction- hence causing the difference in the direction of the torques in the two cases which in turn affects the stability of the system.

Answer 2

is there any equation or principle to determine the direction of the torque??

Answer 3

the right hand screw rule from position vector to the force vector.