ROTATIONAL EQUILIBRIUM AND CENTER OF GRAVITY
Objective:
The objective of this laboratory is to study the condition under which an object is
in rotational equilibrium, and to use second condition of equilibrium to find an unknown
mass and center of gravity. The equipment used to study these conditions are meterstick,
non-uniform meterstick, support stand, three weight hangers, four metal suspension clips,
set of slotted masses, triple beam balance and unknown mass.
Theoretical Background:
An object that is in equilibrium must not be accelerating so that the vector sum of
all forces acting on the object must be ∑ ?⃗ = 0. A rigid body in static equilibrium must
necessarily be in rotational equilibrium.
Torque about some axis of rotation (also called moment of force) results from a
force being exerted at a point not on the axis. Torque is defined as the vector product of
the force and the displacement to the axis: ? = ? ⃗⃗⃗ × ?⃗. Therefore, the magnitude of the
torque is ? = ? × ? × sin(????? ). (The angle between force vector and displacement
vector). Torque is a vector quantity. Its direction is normal to the plane containing r and
F. For convenience, the circular directions of motion that they tend to cause (clockwise
and counterclockwise) designate torques.
A rigid body can rotate about a specific axis in only two directions, clockwise or
counterclockwise.