Problem source

\begin{questionparts}
\item
A wheel consists of a thin 
light circular rim attached by light spokes of length $a$
to a small hub of mass
$m$. The wheel  rolls without slipping
on a rough horizontal table
  directly towards a straight edge of the table.
The plane of the wheel is vertical throughout the motion.
The speed of the wheel is  $u$, where 
 $u^2<ag\,$.

Show  that, after the wheel reaches the edge of the
table and while it is still in contact with the table,
the frictional force on the wheel is zero.
Show also that the hub
 will fall  a vertical distance $(ag-u^2)/(3g)$
before the rim loses contact with the table. 

\item  Two particles, each of mass $m/2$, are attached
to a light circular hoop of radius $a$, at the ends
of a diameter. The hoop rolls without slipping
on a rough horizontal table
 directly towards a straight edge of the table.
The plane of the hoop is vertical throughout the motion.
When the centre of the hoop is vertically above
the edge of the table it has speed $u$, where 
 $u^2<ag\,$, and 
one particle is vertically above the other. 
Show that,  
 after the hoop  reaches the edge of the
table and while it is still in contact with the table,
the frictional force on the hoop 
is non-zero and  deduce that 
the hoop will slip before it loses contact with the table.
\end{questionparts}