Calculate Coriolis acceleration?

Coriolis acceleration is caused by a combination between
the rectilinear motion and circular motion.

It's expression
is:

a = 2*v0*b'(t)

b(t) is the
unit position vector that is pointing in the direction of the motion of an object that
is moving along a line, with speed v0, from the center of a rotating disk. The disk is
moving with constant angular speed, omega.

Now, we'll write
the expression that determine teh position of the moving
object:

R(t) = v0*t*b

Since b
is the unit position vector, we'll describe it's motion with respect to polar
coordinates:

b = cos omega*t*i + sin
omega*t*j

We'll differentiate R(t) and we'll
get:

R'(t) = v0*b(t) +
v0*t*b'(t)

We'll factorize by v0 and we'll
get:

R'(t) = v0*[b(t) +
t*b'(t)]

Now, we'll determine the second derivative to
obtain acceleration:

a(t) = R"(t) = {v0*[b(t) +
t*b'(t)]}'

a(t) = v0*[2b'(t) + t*b"(t)]
(1)

b"(t) = -omega^2*cos omega*t*i - omega^2*sin
omega*t*j

We'll factorize by -
omega^2

b"(t) = -omega^2(cos omega*t*i + sin
omega*t*j)

b"(t) = -omega^2*b(t)
(2)

We'll substitute (2) in
(1):

a(t) = v0*[2b'(t) - t*omega^2*b(t)]
(1)

The first term of a(t)
represents Coriolis
acceleration:

a(t) =
2v0*b'(t)