How many equations of equilibrium are available for the equilibrium of a 2D rigid body?

Question

BlackTom AI · Accepted Answer

To analyze static equilibrium for a 2D rigid body, we must consider the fundamental balance conditions that constrain motion in that plane.
First, think about translational equilibrium: the sum of all forces acting in the x-direction must be zero, which yields one equation, often written as ΣFx = 0.
Next, translational equilibrium in the y-direction requires that the sum of all forces in the y-direction is zero, giving a second equation, ΣFy = 0.
Third, rotational equilibrium about any point (commonly about a chosen origin or the centroid) requires that the sum of moments (torques) due to all forces is zero, giving a third equation, ΣMz = 0.
In a planar (2D) rigid-body problem, there are no other independent equilibrium conditions; forces in directions out of the plane do not exist, and rotations about other axes are not independent in 2D. Therefore, the system of equilibrium equations comprises exactly three independent scalar equations.
This trio of equations is the complete set needed to solve for the unknowns in typical 2D static problems, such as unknown forces and reaction components at supports, provided there are enough independent unknowns to match the three equations.
Note that the actual numerical count can vary if constraints or symmetries reduce the number of independent unknowns, but the standard formulation for a general 2D rigid body in equilibrium yields three independent equations in total.

2025 SP 14:440:221 ENG MECH-STATICS (05 - 08) Lecture 10

How many equations of equilibrium are available for the equilibrium of a 2D rigid body?

View Explanation

Log in for full answers

Similar Questions

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

The break-even point is that at which:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler