The bola

The bola, similar to the North American lasso, is used by South American gauchos to catch small animals by tangling up their legs in the three leather thongs. The motion of the whirling bola through the air is extremely complicated, and would be a challenge to analyze mathematically. The motion of its center of mass, however, is much simpler. The only forces on it are gravitational, so

F_total = m_totalg .

Using the equation F_total = Δp_total/Δt, we find

Δp_total/Δt = m_totalg ,

and since the mass is constant, the equation p_total = m_totalv_cm allows us to change this to

m_totalΔv_cm/Δt = m_totalg .

The mass cancels, and Δv_cm/Δt is simply the acceleration of the center of mass, so

a_cm = g .

In other words, the motion of the system is the same as if all its mass was concentrated at and moving with the center of mass. The bola has a constant downward acceleration equal to g, and flies along the same parabola as any other projectile thrown with the same initial center of mass velocity. Throwing a bola with the correct rotation is presumably a difficult skill, but making it hit its target is no harder than it is with a ball or a single rock.

[Based on an example by Kleppner & Kolenkow.]