Chapter 3
Rotational Kinematics
Abstract Chapter 3 is devoted to rotational motion on horizontal and vertical
planes and on loop-the-loop.
3.1 Basic Concepts and Formulae
If s be the length of the arc and r the radius of the circle, the angle in radians is
given by
θ = s/r
(3.1)
If the angular displacement θ = θ 2 − θ 1 in the time interval t = t 2 − t 1 , then
the average angular velocity
¯
ω =
θ 2 − θ 1
t 2 − t 1
=
θ
t
(3.2)
The instantaneous angular velocity ω is defined as the limiting value of the ratio
as t approaches zero.
ω =
dθ
dt
(3.3)
In case the angular speed is not constant a particle would undergo an angular
acceleration α. If ω 1 and ω 2 are the angular speeds at time t 1 and t 2 , respectively,
then the average acceleration of the particle is defined as
¯
α =
ω 2 − ω 1
t 2 − t 1
=
ω
t
(3.4)
The instantaneous angular acceleration is the limiting value of the ratio as t
approaches zero.
α =
dω
dt
(3.5)
103
Rotational Kinematics
Abstract Chapter 3 is devoted to rotational motion on horizontal and vertical
planes and on loop-the-loop.
3.1 Basic Concepts and Formulae
If s be the length of the arc and r the radius of the circle, the angle in radians is
given by
θ = s/r
(3.1)
If the angular displacement θ = θ 2 − θ 1 in the time interval t = t 2 − t 1 , then
the average angular velocity
¯
ω =
θ 2 − θ 1
t 2 − t 1
=
θ
t
(3.2)
The instantaneous angular velocity ω is defined as the limiting value of the ratio
as t approaches zero.
ω =
dθ
dt
(3.3)
In case the angular speed is not constant a particle would undergo an angular
acceleration α. If ω 1 and ω 2 are the angular speeds at time t 1 and t 2 , respectively,
then the average acceleration of the particle is defined as
¯
α =
ω 2 − ω 1
t 2 − t 1
=
ω
t
(3.4)
The instantaneous angular acceleration is the limiting value of the ratio as t
approaches zero.
α =
dω
dt
(3.5)
103