A rapidly spinning body can respond to a torque mainly by changing the direction of its angular momentum rather than its magnitude. This produces gyroscopic precession.

For a symmetric top spinning rapidly about its symmetry axis, the angular momentum is approximately $$\mathbf L\approx I\omega,\hat{\mathbf e}_3.$$ If gravity exerts torque $$\boldsymbol\tau=\mathbf r\times M\mathbf g,$$ then $$\frac{d\mathbf L}{dt}=\boldsymbol\tau.$$ When $\boldsymbol\tau$ is approximately perpendicular to $\mathbf L$, it turns the vector without strongly changing its length.

For steady precession at rate $\Omega$ around the vertical, $$\left|\frac{d\mathbf L}{dt}\right|=\Omega L\sin\theta,$$ while the gravitational torque magnitude is $$\tau=Mgr\sin\theta.$$ Equating them gives $$\Omega=\frac{Mgr}{L}\approx\frac{Mgr}{I\omega}.$$ A faster-spinning top therefore precesses more slowly under the same gravitational torque.

This result explains a behavior that looks paradoxical if one thinks only in terms of force causing motion 'in its own direction'. Torque changes angular momentum vectorially. The resulting motion depends on the existing angular momentum as well as the applied torque.

Real tops can also nutate, and slow spin invalidates the simple steady-precession approximation. The central insight remains: precession is the geometric consequence of $d\mathbf L/dt=\boldsymbol\tau$ when a torque acts transverse to a large angular momentum.