Discs connected by a belt

A belt (or a chain, as on a bicycle) wraps around two discs and transmits the motion between them. If it does not slip, the rim points in contact with the belt move at the same tangential velocity. Unlike gears, however, the two discs turn in the same direction: the belt that “leaves” one disc enters the other, dragging it along in the same direction.

Principle — Discs connected by a belt

Two discs connected by a belt have tangential velocities equal in magnitude: $|v_1| = |v_2| \;\;\Rightarrow\;\; |\omega_1|\,r_1 = |\omega_2|\,r_2$ and $\omega_1, \omega_2$ have the same sign (both clockwise or both anticlockwise).

The relation between the magnitudes is identical to that for gears: the belt, like rim contact, imposes the same tangential velocity. The only — crucial — difference is the sign.

Gears vs belt: watch the sign!

The difference between gears and a belt is only the sign of $\omega$:

• Gears (rim contact): opposite directions. One disc reverses the other’s direction of rotation.
• Belt/pulley: same directions. The belt transmits the motion while keeping the direction of rotation.

Links

Topics: Dinamica Concepts: Velocità angolare Objects: Ingranaggi e dischi coassiali · Puleggia

Related exercises: Proof of centripetal acceleration · Centripetal acceleration of Earth’s rotation · Ranking points on a rotating disc