= Pulley coupled to a rolling disc
{title2=$q=g(m-M\sin\theta)/(m+3M/2)$}
A hanging <mass> $m$ pulls the centre of a uniform disc of <mass> $M$ up an incline of angle $\theta$, using a light string and light frictionless pulley. If the disc rolls without slipping and the string is parallel to the slope, its effective translational <mass> is $M+I/a^2=3M/2$. With downward hanging <acceleration> $q$, $q=g(m-M\sin\theta)/(m+3M/2)$. <Static friction> has signed downslope component $Mq/2$ and supplies the rolling <torque>. The <acceleration> threshold is unchanged from a sliding block, although rotational inertia reduces the magnitude.
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