A few things on the go here but yes. For rotating things it's polar moment of Inertia or how hard to rotationally accelerate something. Unsprung weight is similar, the suspension of a car cannot react as quickly or control motion as efficiently when all that unsprung weight is trying to bounce around.He is absolutely correct, swing weight has much to do to with it. In some applications its referred to as unsprung weight.
Carbon bike wheels
Aluminum spoke nipples
Forged wheels
all add lightness at right area which enhances efficiency
One of the reasons Volant skis got a bad rap for being heavy, it wasn't because they were much heavier but because their mass went from tip to tail where most other skis the mass was underfoot and not at the extremities.
Bottom line, light weight is often more lively and easier to control.