§ 28. Coriolis Force & Motion in a Rotating Reference Frame (Grade 10–11 · Uni)
Trajectory deflection of a body moving on a rotating platform, inertial forces. A body moving radially in an inertial frame traces a curved spiral in a rotating frame under the action of the Coriolis inertial force.
Theory Summary & Scientific Mechanism
Newton’s laws take their standard form only in inertial reference frames. When observing motion from a rotating non-inertial platform with angular velocity Ω, two fictitious inertial forces appear in the rotating frame: the centrifugal force F_cf = -m[Ω × [Ω × r]] and the Coriolis force F_C = -2m[Ω × vᵣel].
In the stationary laboratory frame (shown by the straight dashed reference line in 3D), a frictionless puck launched radially outward at speed vᵣ moves in a perfect straight line. Meanwhile, the turntable rotates beneath it through angle Δφ = Ω t, so the trace scribed on the disk forms an Archimedean spiral φ(r) = -(Ω)/(vᵣ)r with lateral deflection s ≈ Ω vᵣ t².
Because -2m[Ω × vᵣel] acts perpendicular to vᵣel, it performs no work (F_C · vᵣel = 0) yet deflects trajectories to the right in the Northern Hemisphere (Ω_z > 0), driving cyclonic weather systems, ocean gyres, and the precession of Foucault’s pendulum.
Everyday Analogy
Try rolling a ball straight across a spinning playground merry-go-round: to riders on the platform, the ball mysteriously curves sideways! On our rotating Earth, this Coriolis force swirls hurricanes and slowly rotates Foucault’s pendulum.
Interactive Question & Derivation
A puck is launched radially outward from the center of a horizontal platform rotating counterclockwise (ω pointing upward). In which direction is the puck deflected relative to the rotating platform?
- A: To the right relative to its velocity vector vᵣel (clockwise), since F_Cor = -2m[ω×vᵣel]
- B: To the left in the direction of platform rotation, because the platform drags it along
- C: Strictly along the radius without any lateral deflection
Study Hint: In the Northern Hemisphere, in which direction (right or left relative to velocity v) does the Coriolis force F_C = -2m[Ω×v] deflect a moving body?
Proof & Explanation: In a reference frame rotating with angular velocity ω, any moving body experiences the Coriolis inertial force F_Cor = -2m[ω×vᵣel]. By the right-hand rule, when ω points upward (Northern Hemisphere / counterclockwise rotation), the Coriolis force is perpendicular to vᵣel and deflects the trajectory to the right of the motion direction. Since F_Cor ⊥ vᵣel, its mechanical work is zero.
Key Equations & 3D Simulation Parameters
a_Cor = 2 ω vᵣel, F_Cor = 2m ω vᵣel, Δ s_⊥ ≈ ω vᵣel t²
- Platform angular speed ω: -2.4 … 2.4 rad/s (default: 1.2 rad/s)
- Launch radial speed v₀: 1.2 … 4 m/s (default: 2.5 m/s)
- Sphere mass m: 0.5 … 3 kg (default: 1.5 kg)
- Initial offset from center r₀: 0 … 1.5 m (default: 0.2 m)