Coaxial discs

Two discs mounted on the same axle, “stacked” like cylinders one on top of the other, are forced to rotate together: they are rigidly coupled. They therefore have the same angular velocity, but points on their rims have different tangential velocities, because the radii are different.

Principle — Coaxial (rigidly coupled) discs

Two rigidly coupled discs have the same angular velocity, identical in magnitude and sign: $\omega_1 = \omega_2$ but in general $|v_1| \neq |v_2|$, because $v = \omega\,r$ and $r_1 \neq r_2$.

This is the complementary case to gears. There it was the tangential velocity that was shared and $\omega$ that changed; here it is $\omega$ that is shared and the tangential velocity that changes with the radius. A point on the outer rim (large radius) covers more distance in the same time than a point on the inner rim (small radius), even though it “turns” with the same angular rate.

This is the principle by which an angular velocity is transferred from one disc to another without altering it: by mounting them on the same axle. Combined with gears and belts, it allows arbitrary transmission chains to be built.

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

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