Static equilibrium occurs when an object is at rest and the sum of all forces and torques acting on it is zero. This means both the linear and rotational motions are in balance.
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For an object to be in static equilibrium, the vector sum of all forces acting on it must be zero: $\sum \mathbf{F} = 0$.
The sum of all torques acting on the object about any axis must also be zero: $\sum \tau = 0$.
An object in static equilibrium does not accelerate; both its linear and angular accelerations are zero.
Static equilibrium problems often involve analyzing forces such as tension, normal force, friction, and weight.
Solving static equilibrium problems typically requires breaking down forces into components and using conditions for both translational and rotational equilibrium.
Review Questions
What conditions must be met for an object to be in static equilibrium?
How do you determine if the sum of torques acting on a system is zero?
In a static equilibrium problem, why is it important to break down forces into their components?
A measure of the force that can cause an object to rotate about an axis. It is calculated as the product of the force and the lever arm distance from the axis: $\tau = r \times F$.