Not understood the concept of balancing the stick and a mass on it on the palm. Please explain how the Torque and the length of the particle from the center of mass plays a role in making it balanced?

The magnitude of torque depends on three quantities: the force applied, the length of the lever arm connecting the axis to the point of force application, and the angle between the force vector and the lever arm. In symbols:

where

? is the torque vector and ? is the magnitude of the torque,

r is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and r is the length (or magnitude) of the lever arm vector,

F is the force vector, and F is the magnitude of the force,

× denotes the cross product,

? is the angle between the force vector and the lever arm vector.

The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage.