Release a hoop, a solid disk and a solid sphere from the top of the same ramp at the same instant, and they do not arrive together.

The race#

What does enter is how far the mass sits from the axis. For rotation, mass is replaced by the moment of inertia:

$$I = \sum m_i r_i^2 = k\,MR^2$$

The shape factor $k$ is $1$ for a hoop, $\tfrac{1}{2}$ for a disk and $\tfrac{2}{5}$ for a solid sphere.

Why shape decides#

A rolling body pays for two motions out of one drop: it travels and it spins. Rolling ties them together, $v = \omega R$, and the share that goes into spinning, $k/(1+k)$, is lost to forward motion. That leaves

$$v = \sqrt{\frac{2gh}{1+k}}, \qquad a = \frac{g\sin\theta}{1+k}$$

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What friction does#

Something has to spin each body up. A force turns things through its torque, $\tau = rF\sin\phi$, and $\tau = I\alpha$ plays the role of $F = ma$. Here the torque comes from static friction at the contact point.

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What comes next#

You raced three shapes and found that only the spread of their mass counts. Next we let an object change its own shape while spinning, and find a quantity that holds steady when everything else changes.