# Video: The Equilibrium of Two Couples

If the couples 𝑀₁ and 𝑀₂ are in equilibrium, where 𝑀₁ = 50𝑘, then find the value of 𝑀₁ − 𝑀₂ = ＿.

01:18

### Video Transcript

If the couples 𝑀 sub one and 𝑀 sub two are in equilibrium, where 𝑀 sub one equals 50𝑘, then find the value of 𝑀 sub one minus 𝑀 sub two equals what.

The key point in this statement is that 𝑀 sub one and 𝑀 sub two are in equilibrium. Physically, 𝑀 sub one and 𝑀 sub two are force pairs that potentially exert a torque on a body. The fact that 𝑀 sub one and 𝑀 sub two are in equilibrium means two things. First, it means they have equal magnitudes. And second, it means they are opposites of one another.

So when we say 𝑀 sub one and 𝑀 sub two are in equilibrium, we mean that they don’t exert a net force on the body, if any, on which they act. In other words, the body itself is also in equilibrium.

Using point number two and the fact that 𝑀 sub one is equal to 50𝑘, we know that 𝑀 sub two must equal negative 50𝑘. So 𝑀 sub one minus 𝑀 sub two must equal 50𝑘 minus minus 50𝑘, or 100𝑘. That’s the value of 𝑀 sub one minus 𝑀 sub two.