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d θ
2
α = . 2-51
dt 2
The line of action of αis the same as that for ω, Fig. 2-18,a;
however, its sense of direction depends on whether ω is increasing or
decreasing. If ω is decreasing, then is called an angular deceleration
and therefore has a sense of direction which is opposite to ω.
By eliminating dt from Eqs. 2-49 and 2-50, we obtain a
differential relation between the angular acceleration, angular velocity,
and angular displacement, namely,
α d =θ ωω 2-52
d
The similarity between the differential relations for angular
motion and those developed for rectilinear motion of a particle
(v = ds / dt , a = dv / dt and ads = vdv) should be apparent.
Constant Angular Acceleration. If the angular acceleration of
the body is constant, α = α c , then Eqs. 2-49, 2-50, and 2-52, when
integrated, yield a set of formulas which relate the body’s angular
velocity, angular position, and time. These equations are similar to
equations used for rectilinear motion. The results are
ω ω= 0 + t α 2-53

1
θ θ + ω t + t α 2-54
2
=
0
0
2
2
−
ω = ω + 2(αθ θ 0 ) 2-55
2
0
here θ and ω are the initial values of the body’s angular position and
0
0
angular velocity, respectively.
49 Motion of Body’s Point P
As the rigid body in Fig. 2-19,a rotates, point P travels along a
circular path of radius r with center at point O. This path is contained
within the shaded plane shown in top view, Fig. 2-19,b.
Position and Displacement. The position of P is defined by the
position vector r, which extends from O to P. If the body rotates dθ
then P will displace ds = rdθ .

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