When an object isn't changing its velocity, either because it's chillin' at rest or moving in a straight line (called translational motion) at a constant speed, we say it's in translational equilibrium.

Remember how Newton's first law says an object at rest stays at rest and an object in motion stays in motion unless acted upon by an external force? And his second law says that force is equal to mass times acceleration? Well, when an object's in translational equilibrium, there's zero total force acting on it because its velocity isn't changing.

Let's break down some scenarios

• When two forces of equal size pull an object in opposite directions, they cancel each other out. Imagine a tug of war where both sides are equally strong, so the rope doesn't move.
• When two forces of equal size act at different angles, they don't cancel out. It's like two people pulling a sled from different directions. The sled will move in the direction of the combined (or resultant) force.

When more than two forces act on an object, things can get complicated. You need to add up all the forces (resolve the vectors) in each direction and check if they cancel out.

Say a small ring is hanging from a spring balance with a weight attached to it and also a string pulling it sideways (like in a game of 3-way tug-of-war). For the ring to remain still (equilibrium), all forces in every direction need to cancel out. This is the magic of vector resolution.

Here's a cool trick - if you draw all the forces on a system so that they form a closed triangle, you know the system is in translational equilibrium. This is known as the triangle of forces.