eloquent logic - equilibrium

Legend

F	=	Force
d	=	distance

Formulas

F = 0

1) F_x = 0 2) F_y = 0 3) = 0	1) all horizontal forces add up to zero 2) all vertical forces add up to zero 3) all twisting, rotating forces add up to zero (called torque, )
= dF	= Torque d = distance perpendicular from pivot point to point where force is applied F = force applied

Just as we define which direction is positive and negative for x and y directions, we must define which direction of rotation is positive or negative for torques. These symbols (

) defines whether clockwise or counter-clockwise is positive.

When writing torque equations, you must choose the center of rotation first. It can be chosen anywhere you want; however, you will find that in solving equilibrium problems, wisely chosen centers of rotation can make getting the answer more simple.

Diagram

Use the below table by referring to the diagram above.

center of rotation	direction of rotation	torque equation
A		= 0: +m₂gd₁ - F_Nd₂ + m₃gd₃ = 0
B		= 0: -m₂gd₄ + m₃gd₅ + m₁gd₂ = 0
C		= 0: +F_Nd₄ - m₃gd₆ - m₁gd₁ = 0

Interactive Lab

Problems