Transmission of rotational and translational motion
In machines rotation is passed from one wheel to another. In a friction drive two wheels are pressed together and friction makes the second one turn in the opposite direction; in a belt drive the wheels (pulleys) are joined by a tight belt. In both cases, with no slipping, the linear speeds at the rims are equal: υ₁ = υ₂, i.e. ω₁R₁ = ω₂R₂, so ω₁/ω₂ = ν₁/ν₂ = R₂/R₁: the smaller wheel turns faster. In a gear drive the number of teeth passing the contact point per unit time is the same: N₁ν₁ = N₂ν₂, so ν₁/ν₂ = N₂/N₁. Wheels fixed on one axle have the same angular speed, while their linear speeds are proportional to their radii. A gear drive does not slip and transmits large power; a friction drive suits only small power. A sewing machine and the crank–connecting-rod mechanism of an engine convert rotation into reciprocating (translational) motion.
Only with the teacher: count the teeth on a bicycle’s pedal sprocket and on the rear sprocket and compute their ratio (do not touch the chain; the bicycle must stay still). Predict how many times the rear wheel turns for one turn of the pedals.