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Boundless Physics
Static Equilibrium, Elasticity, and Torque
Conditions for Equilibrium
Physics Textbooks Boundless Physics Static Equilibrium, Elasticity, and Torque Conditions for Equilibrium
Physics Textbooks Boundless Physics Static Equilibrium, Elasticity, and Torque
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 10
Created by Boundless

Two-Component Forces

In equilibrium, the net force and torque in any particular direction equal zero.

Learning Objective

  • Calculate the net force and the net torque for an object in equilibrium


Key Points

    • In equilibrium, the net force in all directions is zero.
    • If the net moment of inertia about an axis is zero, the object will have no rotational acceleration about the axis.
    • In each direction, the net force takes the form: $\sum \textbf{F}=m\textbf{a}=0$ and the net torque take the form: $\sum \boldsymbol{\tau}=I\boldsymbol{\alpha}=0$ where the sum represents the vector sum of all forces and torques acting.

Term

  • equilibrium

    The state of a body at rest or in uniform motion, the resultant of all forces on which is zero.


Full Text

An object with constant velocity has zero acceleration. A motionless object still has constant (zero) velocity, so motionless objects also have zero acceleration. Newton's second law states that:

$\sum \textbf{F}=m\textbf{a}$

so objects with constant velocity also have zero net external force. This means that all the forces acting on the object are balanced -- that is to say, they are in equilibrium.

This rule also applies to motion in a specific direction. Consider an object moving along the x-axis. If no net force is applied to the object along the x-axis, it will continue to move along the x-axis at a constant velocity, with no acceleration .

Car Moving at Constant Velocity

A moving car for which the net x and y force components are zero

We can easily extend this rule to the y-axis. In any system, unless the applied forces cancel each other out (i.e., the resultant force is zero), there will be acceleration in the direction of the resultant force. In static systems, in which motion does not occur, the sum of the forces in all directions always equals zero. This concept can be represented mathematically with the following equations:

$\sum F_{x}=ma_{x}=0$

$\sum F_{y}=ma_{y}=0$

This rule also applies to rotational motion. If the resultant moment about a particular axis is zero, the object will have no rotational acceleration about the axis. If the object is not spinning, it will not start to spin. If the object is spinning, it will continue to spin at the same constant angular velocity. Again, we can extend this to moments about the y-axis as well. We can represent this rule mathematically with the following equations:

$\sum \tau_{x}=I\alpha_{x}=0$

$\sum \tau_{y}=I\alpha_{y}=0$

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