Page 80 - C:\Users\trainee\AppData\Local\Temp\msoEAA3.tmp

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

Rearranging the like terms in equation (2.61), we get:

2
2
d r d r dr dω
2

= r + 2 ωT − ω rr + rT
dt 2 dt 2 dt dt
The above expression can also be written to get the four accelerations as:
2
2
2
d r d r dr dθ dθ 2 d θ

= r + 2 rr + rT
T −
dt 2 dt 2 dt dt dt dt 2
In summary the accelerations for curvilinear motion is tabulated as follows:
Accelerations In the form of derivatives In the form of vectors

Radial acceleration d r d r
2
2
dt 2 r dt 2 r
Coriolis dr dθ 2 ω × V

2 T
dt dt
Centripetal acceleration dθ 2 ω × ω × r
rr
dt

2
Tangential acceleration d θ
dω

rT × r
dt 2 dt

Example 1: find the ratio of maximum to minimum centripetal acceleration for a particle
negotiating an elliptical curve at constant velocity, as shown in [Fig 2.68].

[Fig 2.68: Point traversing an elliptical path]

Page 80 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,