# Calculate Coriolis acceleration?

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### 1 Answer

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)**