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Document Title
Fundamentals of Stress and Vibration Chapter Title
[A Practical guide for aspiring Designers / Analysts] 2. Engineering Mechanics

However, a fourth acceleration is produced due the radial and angular velocities. This acceleration is
called the “Coriolis” acceleration. The Coriolis acceleration is responsible for several natural and
mechanical phenomena. Example, cyclones, missiles missing the target, ocean currents, turbulence
in flows, mechanisms (quick return motion mechanism) etc.

Therefore, finding the acceleration becomes a challenge, these accelerations could be:

ü Radial acceleration d r dt due to change of radius with respect to time.
2
2

ü Tangential acceleration due to rate of change of angular velocity dω dt .

2
ü The centripetal acceleration (V r) is variable, as both the radii and velocity change from
point to point.
ü Since there is a rate of change of radius and the radius itself is rotating (as there is angular
motion), the Coriolis 2Vω component comes into play.

Let us now derive the four accelerations for curvilinear motion.

Consider a point on the curvilinear motion path, which has an instantaneous radius vector r , as
shown in [Fig 2.67].

[Fig 2.67: Curvilinear motion of a particle]

Mathematically, the radius vector is given by: r = rr .

The first step is to find the rate of change of the radius vector along the curvilinear path. This is
given by, the derivative of the radius vector with respect to time:

dr dr dr
= r + r - - - - (2.56)
dt dt dt
The unit radius vector r is rotating at a certain angular rate dθ dt . Therefore, the rate of

change of the unit radius vector is represented as follows.

dr dr dθ
= - - - - (2.57)
dt dθ dt

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