A fixed pivot constrains a point of a rigid body to remain stationary in a specified frame while permitting rotation. With an ideal pivot at $O$, the reaction force acts at $O$ and contributes no torque about that point. Angular momentum balance is therefore conveniently written about $O$.

For planar rotation about a fixed axis, $I_O\ddot{\theta }={\tau }_O$. A uniform rod of length $\ell$ pivoted at one end has $I_O=m{\ell }^2/3$; gravity supplies the restoring torque when it hangs downward. A frictional pivot can also exert a couple, so zero reaction torque is an idealization to state explicitly.

A rigid-body twist represents an instantaneous rigid body velocity field by a pair of three-dimensional vectors, conventionally ordered $(\mathbf{\omega },\mathbf{v})$. In a stated reference frame, $\mathbf{\omega }$ is angular velocity and $\mathbf{v}$ is the velocity field evaluated at that frame's origin. Every point at position $\mathbf{x}$ has instantaneous velocityThe linear component therefore need not be the center of mass velocity. Both components must use the same coordinate frame; their physical units also differ.^[ref]

The formula follows by differentiating the point position $\mathbf{x}=R(t)\mathbf{X}+\mathbf{p}(t)$, where $R$ is a rotation matrix and $\mathbf{X}$ is fixed in the body. The skew-symmetric matrix $\dot{R}{R}^T$ acts as the cross product with $\mathbf{\omega }$. HenceAt the body's chosen origin $\mathbf{x}=\mathbf{p}$, this correctly returns $\dot{\mathbf{p}}$. Moving the reference origin by a fixed vector $\mathbf{a}$, without changing its axes, gives ${\mathbf{v}}^{\prime }=\mathbf{v}+\mathbf{\omega }\times \mathbf{a}$, with the same angular velocity. The numbers change while the physical velocity field is unchanged.

When $\mathbf{\omega }\ne 0$, define the screw pitch and a point on the instantaneous axis byThe vector triple-product identity gives $\mathbf{u}(\mathbf{q})=h\mathbf{\omega }$. Points on $\mathbf{q}+\lambda \mathbf{\omega }$ share that axial velocity; off-axis points additionally rotate about it. A constant rigid-body twist therefore generates a screw motion. Zero angular velocity instead gives pure rigid-body translation, for which these divisions are not defined.

For an original numerical example take $\mathbf{\omega }=(0,0,2)rad/s$ and $\mathbf{v}=(1,0,0.4)m/s$. At $(0,1,0)\mathrm{m}$ the velocity is $(-1,0,0.4)m/s$. The axis passes through $\mathbf{q}=(0,0.5,0)\mathrm{m}$, with axial speed $0.4m/s$ and screw pitch $h=0.2m/rad$. If the twist stays constant for a revolution, the axial advance is $2\pi h\simeq 1.257\mathrm{m}$.

A twist describes instantaneous motion; it is not generally a six-coordinate finite pose or its ordinary derivative. Its reference-frame convention matters when using a robot's measured joint rates to predict endpoint velocity.

Right ventricular ejection fraction is the fraction of the right ventricle's end-diastolic volume that leaves its cavity during systole. If $V_{\mathrm{ED}}$ is the filled volume and $V_{\mathrm{ES}}$ the residual end-systolic volume,where $\mathrm{SV}$ is stroke volume. It is a dimensionless ratio, usually reported as a percentage. The filling and ejection phases must refer to the same cardiac cycle; the tricuspid valve and pulmonary valve determine the normal direction of blood flow.^[ref]

For example, $V_{\mathrm{ED}}=120$ mL and $V_{\mathrm{ES}}=60$ mL give $\mathrm{SV}=60$ mL and $\mathrm{RVEF}=50\%$. A second right ventricle with volumes 200 and 100 mL also has $50\%$ right ventricular ejection fraction, but its stroke volume is 100 mL. A fraction describes emptying relative to the initial volume; it does not specify an absolute cardiac output.

A practical volumetric approach uses magnetic resonance imaging at multiple phases and image segmentation to estimate the two cavity volumes.^[ref] Consistent boundary choices matter because two measurements enter one ratio. For small volume errors, direct differentiation givesShared boundary errors need not act like independent errors. Moreover, cavity volume loss includes any backward flow through an incompetent tricuspid valve; the formula alone does not prove that all of the calculated stroke volume reached the pulmonary trunk.

Ribosomal protein L22 is a bacterial ribosomal protein with a tunnel-facing contribution to the environment encountered by an emerging polypeptide chain. Its molecular identity and its role in a particular regulatory stall are separate levels of description: showing that a residue affects one nascent-chain response does not establish that every translation event is affected equally.

A 2002 genetic experiment provided a concrete functional connection. Mutations bypassing SecM-dependent elongation arrest were found in ribosomal protein L22 and 23S ribosomal RNA. The altered residues faced the narrow constriction of the ribosomal exit tunnel. Their positions and effects supported an interaction between that region and the nascent chain.^[ref]

An original comparison illustrates how to distinguish a sequence-sensitive effect from a general failure of translation. Suppose an assay measures the arrested fraction for an arrest-capable peptide and for a control peptide:These invented values show a change associated mainly with the arrest-capable sequence. Measuring only its0.8-to-0.2 change would omit the comparison supplied by the control. Such a pattern would motivate a sequence-sensitive explanation, but additional checks of assembly, abundance and general translation competence would still be needed.

The experiment also separates an affected protein component from the larger molecular apparatus. L22 acts within a ribosome containing ribosomal RNA and many other components. A mutation's effect can depend on that surrounding structure and on the peptide being synthesized. Functional perturbation and structural location therefore complement one another without making the isolated protein the entire arrest mechanism.

Ribosomal protein S1 is an RNA-binding ribosomal protein that helps many bacterial messenger RNAs engage the small ribosomal subunit for translation initiation. In Escherichia coli, S1 is a single polypeptide chain containing six related S1 RNA-binding domains. The whole protein and its repeated domain are distinct concepts; an S1 domain also occurs in proteins outside the ribosome.^[ref][ref]

A 2013 study tested how S1 helps structured messages enter the decoding region. Researchers compared intact, S1-depleted and reconstituted 30S subunits, including S1 variants missing selected domains. Binding measurements and toeprinting distinguished RNA association from formation of a correctly positioned 30S initiation complex. The experiments showed different domain requirements for different messages; the first three domains were important for handling the tested structured rpsO message.^[ref]

For an illustrative control, suppose removing S1 reduces an initiation-associated signal for a folded message but changes a simpler message little. Restoring the signal by adding back intact S1 would support a message-dependent contribution. General loss of ribosome assembly or unequal RNA amounts could also change the readout, so they require separate checks. An RNA-binding measurement alone does not establish completed translation; a domain count alone does not specify how many functional binding sites a protein supplies.

Antisense RNA is RNA complementary to a specified sense transcript or part of it, allowing antiparallel base pairing with that target. Sense and antisense are relational labels: the target and strand orientation must be specified. Antisense molecules can occur naturally or be produced experimentally, and complementary pairing can influence transcript processing, stability or access to translation machinery.^[ref]

For an original sequence example, a target segment $5^{\prime }\text{-}\mathrm{AUGCC}\text{-}{3}^{\prime }$ pairs with $3^{\prime }\text{-}\mathrm{UACGG}\text{-}{5}^{\prime }$. Written in the usual $5^{\prime }$-to-$3^{\prime }$ direction, the antisense sequence is $5^{\prime }\text{-}\mathrm{GGCAU}\text{-}{3}^{\prime }$. Merely replacing each target letter by its complement without reversing the written direction gives a different sequence.

A tomato experiment expressed Antisense RNA directed against 1-aminocyclopropane-1-carboxylate synthase, a precursor-forming enzyme in ethylene biosynthesis. Ripening was inhibited, and supplying ethylene or propylene reversed the effect. The intervention and rescue linked altered expression to a physiological signal pathway, rather than treating ripening and ethylene production as a simple correlation.^[ref]

Complementarity alone is not a quantitative prediction of suppression. Target accessibility, expression levels and the cellular machinery determine the outcome. An Antisense RNA construct, an observed change in target protein and an observed phenotype therefore provide different pieces of evidence.

Negative-sense RNA is RNA whose sequence is complementary to the corresponding messenger RNA sequence. “Negative” specifies orientation relative to a coding message; it does not mean negative electric charge, damage, or lack of biological function. A negative-sense viral genome must first be copied into a message-compatible Positive-sense RNA before its encoded proteins can be made by translation.

For a short illustrative message $5^{\prime }\text{-AUGGCU-}{3}^{\prime }$, the complementary template is $3^{\prime }\text{-UACCGA-}{5}^{\prime }$, equivalently $5^{\prime }\text{-AGCCAU-}{3}^{\prime }$ when written in the conventional direction. The strands are complementary and antiparallel. Simply reversing the letters, without exchanging complementary bases, would not produce the negative-sense template. This small example shows why both sequence and direction matter.

The requirement creates a startup problem for a virus: if the entering genome cannot itself serve as messenger RNA, how can it make the enzyme needed to copy that genome? Vesicular stomatitis virus solves this by carrying an RNA-dependent RNA polymerase in its viral particle. In the 1970 experiment by D. Baltimore, A. S. Huang and M. Stampfer, virion preparations incorporated supplied ribonucleotide substrates into new RNA; the main product was complementary in sequence to the viral genome.^[ref]

This experiment connects a sequence classification to physical machinery packaged with the genome. Positive-sense RNA and Negative-sense RNA describe the relation of an RNA region to the coding message; identifying the sense does not by itself specify all details of genome segmentation, replication intermediates or transcription control.

Positive-sense RNA has the sequence orientation of a corresponding messenger RNA, rather than being its complementary template. In a positive-sense RNA virus, the entering genome can provide a coding message for translation, allowing production of the viral machinery that subsequently copies RNA. This is a sequence-and-function distinction, not a claim about the molecule's electric charge.

For example, a positive-sense coding segment $5^{\prime }\text{-AUGGCU-}{3}^{\prime }$ begins with the codons AUG and GCU in that reading frame. Its complementary negative-sense template is $3^{\prime }\text{-UACCGA-}{5}^{\prime }$. A polymerase copying that template produces the positive-sense sequence. Both directions and complementary bases are needed; reversing a string alone is insufficient.

Early experiments with poliovirus made the informational role of viral RNA concrete. Isolated RNA introduced under suitable conditions infected human cell monolayers and yielded virus of the original type. Ribonuclease abolished the isolated RNA's infectivity, whereas intact-virus infectivity resisted the same enzyme treatment, supporting the interpretation that exposed RNA carried the infectious genetic information.^[ref]

This does not mean naked RNA naturally enters every cell efficiently; the experiment depended on preparation and exposure conditions. It also does not eliminate the need for an RNA-dependent RNA polymerase during genome replication. The distinction from Negative-sense RNA concerns how the initial coding message is obtained, rather than whether replication ever requires a complementary strand.

An RNA cyclic phosphate end is an RNA terminus in which a phosphate group links the $2^{\prime }$ and $3^{\prime }$ oxygens of the terminal ribose, forming a small cyclic phosphodiester bond arrangement. The ring is local to the terminal nucleotide; the whole RNA chain need not be circular. This end chemistry differs from both a free $3^{\prime }$ hydroxyl group and an ordinary terminal $3^{\prime }$ phosphate.^[ref]

The difference matters for RNA ligation. A 2012 study showed that RtcB opens the cyclic end to a $3^{\prime }$ phosphate before joining it to an RNA $5^{\prime }$ hydroxyl group. The reactions depended on GTP and enzyme guanylylation. Researchers followed labelled products over time using denaturing polyacrylamide gel electrophoresis, distinguishing starting cyclic ends, transient products and joined RNA.^[ref]

As a measurement example, two four-nucleotide RNA molecules could both spell AUGC while one ends in a free $3^{\prime }$ hydroxyl group and the other in a cyclic phosphate. A readout reporting only their letters would merge them, even though a reaction requiring the free hydroxyl group could distinguish them. Nucleotide sequence therefore does not completely specify terminal chemistry, and terminal chemistry can determine which RNA molecules an assay records.