A disk of radius 1 is rotating in the counterclockwise direction at a constant angular speed ω. A particle starts at the center of the disk and moves toward the edge along a fixed radius so that its position at time t, t ≥ 0, is given by r(t) = tR(t), where

R(t) = cos ωt i + sin ωt j

(a) Show that the velocity v of the particle is

v = cos ωt i + sin ωt j + tv_d

where v_d = R'(t) is the velocity of a point on the edge of the disk.

(b) Show that the acceleration a of the particle is

a = 2v_d + ta_d

where ad − R0std is the acceleration of a point on the edge of the disk. The extra term 2v_d is called the Coriolis acceleration; it is the result of the interaction of the rotation of the disk and the motion of the particle. One can obtain a physical demonstration of this acceleration by walking toward the edge of a moving merry-go-round.

(c) Determine the Coriolis acceleration of a particle that moves on a rotating disk according to the equation

r(t) = e^−t cos ωt i + e^−t sin ωt j