Lower inertia means it moves faster, right?

[Lo.Lee.Ta.]

I was working out a conceptual question that asks: if a disk and a hoop of equal mass and radius start from the top of a ramp, are realeased at the same time, and roll without slipping, which one reaches the bottom of the ramp first?

Disk: I = 1/2(m)(r^2)

Hoop: I = mr^2

So the inertia of the disk ends up being lower. Lower inertia means the disk moves faster, right?

 

[lewando]

"It accelerates faster" would be more correct. Looking at τ=Iα, for the the two cases with equal torque (τ) applied, if I (moment of inertia) was smaller, then α, (angular acceleration) would have to be larger.