A ball bearing transfers loads through rolling spherical elements between two races. The no-slip conditions at both contacts determine the translation and spin of each ball; these are generally not the same angular velocity.

For a uniform sphere struck horizontally with impulse $J$ at height $d$ above its centre, $u_0=J/M$ and clockwise spin ${\Omega }_0=5Jd/(2M{a}^2)$. friction brings the contact slip $u-a\Omega$ to zero. The final rolling speed is $u_f=5J(1+d/a)/(7M)$, independent of a positive constant friction coefficient; friction can accelerate an initially overspinning centre of mass.

A circular body of radius $r$ rolls inside a circular track of radius $R$. Let $\theta$ be the track's material rotation, $\varphi$ the absolute angle of the line joining the two centres, and $\psi$ the inner body's absolute spin angle, all with one consistent orientation. Equating contact-point velocities gives the displayed constraint. Translation of the track's centre cancels from that equality. A stationary track gives $\dot{\psi }=-(R-r)\dot{\varphi }/r$.

With downward speed $v$, downward relative exhaust speed $v_E>0$ and mass $M=M_0-\alpha t$, the ideal vertical equation is $\dot{v}=g-\alpha v_E/M$. Integration gives $v=v_0+gt+v_E\log (M/M_0)$. Height follows from $\dot{h}=-v$; its touchdown condition must be imposed together with the final fuel fraction.

Sequencing designed to span long portions of individual RNA molecules or derived Complementary DNA. Linking distant exons on one molecule helps resolve complete transcript isoforms, while per-base errors and sampling depth still require control.

Profiling RNA from individual isolated cell nucleus preparations. The preparation samples nuclear and often incompletely processed transcripts, so its intron counts are not interchangeable with mature cytoplasmic messenger RNA counts.

Thiol-linked alkylation used with metabolic RNA labelling to identify newly synthesized RNA through characteristic sequencing changes after 4-thiouridine incorporation.^[ref]

Cap analysis of gene expression: sequencing capped RNA ends to characterize start-site usage. Differential survival or capping of transcripts can alter the observed distribution without a matching change in nascent initiation.

A nuclear run-on and capped-end mapping method for characterizing transcription initiation. It is useful for comparing nascent initiation with the surviving mature transcript molecular population.^[ref]

Nanopore sequencing infers a nucleic-acid sequence from changes in electrical current as a strand passes through a nanometre-scale pore. The signal depends on several nearby bases rather than one perfectly isolated base at a time. It supports long reads and direct RNA measurement, but base calling and modification inference require calibrated models. Comparison of conditions can detect altered signal patterns without identifying every chemical modification uniquely. ^[ref]

Transcript assembly reconstructs transcript sequences or exon paths from RNA-derived reads. It can use a reference genome or infer sequences directly from overlaps. Alternative splicing creates shared segments, so a set of individually supported exons does not necessarily determine which full-length combinations occur. Long reads can connect distant exons, but transcript completeness and sequence errors still require evaluation. ^[ref]

RNA-seq differential expression compares transcript abundance between conditions using RNA sequencing data. Counts require normalization and a model that accounts for biological variability as well as sampling. A transcript’s share of all reads can fall even when its absolute abundance is unchanged, if other transcripts increase. Replicate samples, composition effects and cell-type mixtures therefore matter when interpreting an apparent expression change. ^[ref]

Read coverage describes how sequencing reads overlap a target sequence. Per-base depth counts overlapping reads at each position, whereas breadth asks what fraction of target positions receives specified support. For example, high average depth can coexist with an uncovered exon if sampling is uneven. In RNA sequencing, coverage also reflects transcript abundance, processing and library preparation, so absence of reads is not automatically evidence that a genomic region is absent. ^[ref]