Question

The objects listed below are placed at the top of a ramp, and roll down to the bottom without slipping. Assuming that there is no air resistance, rank them in order from fastest average rolling speed to slowest.

Penny, large marble, basketball, and hula hoop

Answer 1

If they do not slip, there is a friction force up the slope resulting in angular acceleration of the rolling thing. Let's call it Fc.
Fc R = torque = I alpha
so
alpha = Fc R/I
BUT
alpha is related to a, the linear acceleration down the slope
alpha = a/R
and the gravity force down the slope - Fc = m a
m g sin theta - Fc = m a
m g sin Theta - Fc = m a
m g sin Theta - I a/R^2 = m a
a (m + I/R^2) = m g sin Theta
a = g sin Theta/ (m + I/R^2)
the bigger I/R^2, the lower a
in other words if the mass is at the outer edge, it goes slowly
The hula hoops has all its mass concentrated at the outer radius, it has the slowest a