The rotational configuration of a rigid body relative to a reference frame. In three dimensions, one marked direction leaves rotation about that direction undetermined.

For a rigid vehicle turning on a level road, with centre of mass height $h$, half track width $a$ and turn radius $R_b$, sufficient static friction supplies centripetal acceleration $v^2/R_b$. The inner and outer wheel normal forces obey $N_i+N_o=Mg$ and $a(N_o-N_i)=Mh{v}^2/R_b$. The inner contact force first vanishes at the displayed speed. The approximation neglects suspension movement and extra torques; inadequate static friction can cause sliding before rollover.

Polyuridylic acid is an RNA polymer whose nucleotides all carry uracil.

An extensional flow stretches material along one or more directions while contracting it along others. A local ideal model of planar extension has velocity $\mathbf{u}=(\dot{ϵ}x,-\dot{ϵ}y,0)$: its rate-of-strain tensor is $\mathrm{diag}(\dot{ϵ},-\dot{ϵ},0)$ and it is an incompressible flow. Uniaxial extensional flow instead contracts both transverse directions. These geometries probe extensional viscosity and can stretch polymers.

The complementary limit of the branching model permits inhibitor binding only to the enzyme-substrate complex: set $K_i\to \infty$, hence $\alpha =1$, with finite $K_i^{\prime }$. Then both $V_{\max ,\mathrm{app}}$ and $K_{M,\mathrm{app}}$ decrease by ${\alpha }^{\prime }$, while their ratio stays fixed. This limit helps distinguish preferential binding to $ES$ in mixed inhibition from exclusive binding to $ES$ in uncompetitive inhibition.

In the branching model, mixed inhibition retains inhibitor binding to both free enzyme and the enzyme-substrate complex. Unequal $K_i$ and $K_i^{\prime }$ shift both apparent parameters; their equality gives pure noncompetitive inhibition. For the chosen unequal case, $I=30\mu \mathrm{M}$ gives $\alpha =4$ and ${\alpha }^{\prime }=2$, hence $V_{\max ,\mathrm{app}}=50\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$ and $K_{M,\mathrm{app}}=40\mu \mathrm{M}$. Because $K_i<K_i^{\prime }$, binding favours free enzyme, and the apparent Michaelis constant increases. Reversing that inequality decreases it.

The limiting behaviour provides a useful diagnostic within this model:Low substrate concentration isolates $\alpha$ through the initial slope; high substrate concentration isolates ${\alpha }^{\prime }$ through the plateau. At $I=30\mu \mathrm{M}$, the chosen competitive inhibition and unequal mixed inhibition examples have the same low-$s$ slope, $1.25\mathrm{mi}{\mathrm{n}}^{-1}$, but different plateaus, $100$ and $50\mu \mathrm{M}\mathrm{mi}{\mathrm{n}}^{-1}$. Measuring only low substrate concentrations would miss that distinction.