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Static Equilibrium of Rigid Bodies

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

What is static equilibrium? Learn about the factors that cause an object to remain stationary, without translating or rotating. Then take a quiz to make sure your understanding hasn't remained static.

What is Static Equilibrium?

What makes a stationary object stay stationary? Why does a parked car stay where it is? Or a wind turbine not rotate that particular minute? It might seem obvious, but there are certain conditions that have to be met for that to happen - for the object to be in static equilibrium.

Static equilibrium is where an object isn't moving because the various influences on that object are in balance (are equal). A rigid body is just an object that has a particular shape that doesn't change. So static equilibrium of a rigid body is the state where a solid object isn't moving, because its influences are balanced.

But what causes an object to be in static equilibrium? There are two conditions that have to be met for this to be the case. The object must be in both translational and rotational equilibrium.

Translational Equilibrium

Translation is where an object moves left or right, forward or back, up or down. It's a movement of the whole object in a particular direction. The object is said to be in translational equilibrium if the forces are balanced in all directions - if the upward forces equal the downward forces, the leftward forces equal the rightward forces, and the forward forces equal the backward forces. The forces are equal, which is why it's called equilibrium.

Equilibrium involves balanced forces
Equilibrium involves balanced forces

For example, let's go back to the parked car. It stays where it is because the forces on it are balanced. The downward force of gravity is balanced by the ground pushing back up on the car. If you walk up to the car and give it a push, but the car doesn't move, it's because your pushing force was balanced by the force of friction - a force caused by the roughness of the ground.

Rotational Equilibrium

But objects don't just move up and down, or left and right, or forward and back. There's one other kind of movement - rotational movement. Rotational motion is where an object stays in position, but twists around a pivot point. This is like how a wheel turns on its axis, or a wind turbine spins when pushed by the air.

A Ferris wheel is an example of rotational motion
A Ferris wheel is an example of rotational motion

Forces make things rotate, just as they make things translate. But for rotation to happen, the force has to be off center. If you find a see-saw in a park, and push it at the very center, nothing will happen. To make the see-saw go up or down, you have to push nearer one of the edges. We call this force at a distance from a pivot point a torque. The harder you push, the greater the torque, and the further from the pivot point you push, the greater the torque.

To move a see-saw, you push near the ends
To move a see-saw, you push near the ends

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