Chapter 4
Rotational Dynamics
Abstract Chapter 4 is concerned with the moment of inertia and rotational motion
on horizontal and inclined planes and Coriolis acceleration.
4.1 Basic Concepts and Formulae
Moment of Inertia/Rotational Inertia (M.I.) or (I)
Table 4.1 Moments of inertia (M.I.) of some regular bodies
Body
Axis
M.I.
Thin rod of length L
Perpendicular to length through centre
m L 2 /12
Perpendicular to length at one end
m L 2 /3
Thin rectangular sheet of sides
a and b
Through centre parallel to side b
m a 2 /12
Through centre perpendicular to sheet
m(a 2 + b 2 )/12
Thin hoop
Through centre perpendicular to plane
of ring
mr 2
Through centre along diameter
mr 2 /4
Thin circular disc
Through centre perpendicular to disc
mr 2 /2
Solid sphere of radius r
About any diameter
2mr 2 /5
Thin spherical shell
About any diameter
2mr 2 /3
Right cone of radius of base r
Along axis of cone
3mr 2 /10
Circular cylinder of length L
and radius R
Through centre perpendicular to axis
m
R 2
4 +
L 2
12
Table 4.2 Translational and rotational analogues
Quantity
Translation
Rotation
Displacement
s
θ
Velocity
v = ds/dt
ω = dθ/dt
Acceleration
a = dv/dt
α = dω/dt
Mass/inertia
m
I
Momentum
p = mv
J = I ω
Impulse
J = Ft
J = τ t
Work
W = Fs
W = τ θ
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