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0593_C04*_fm Page 115 Monday, May 6, 2002 2:06 PM

Kinematics of a Rigid Body 115

A D

θ

B
FIGURE P4.4.2
Rotating disk D, rotation angle θ,
and scribed line AB. φ
line. Show that dφ/dt = dθ/dt and that, therefore, the angular speed and angular acceler-
ation of D may be expressed as:

φ
ω = ddt and α = d 2 φ dt 2

P4.4.3: Refer to Problem P4.4.2. Suppose φ is a function of time t given by:

2
φ=+54t + 8t deg
where t is in seconds. Find the angular speed ω and angular acceleration α of D for t =
(a) 1 sec, (b) 2 sec, and (c) 5 sec.
P4.4.4: See Problem P4.4.3. Find the angle turned through by D from t = 2 to t = 5 sec.

Section 4.5 General Angular Velocity

P4.5.1: Let a body B be moving in a reference frame R such that the angular velocity of B
in R is given by:

R B
ωω = 8n + 4n − 5n rad sec
x y z
where n , n , and n are fixed in B. Let n , n , and n be parallel to the X, Y, Z coordinate
x y z x y z
axes fixed in B as in Figure P4.5.1. Let P and Q be particles of B with coordinates P(1, 2, –3)
and Q(–2, 4, 7), measured in meters. Using Eq. (4.5.2), find:

a. The velocity of P relative to O in R.
b. The velocity of Q relative to O in R.
c. The velocity of P relative to Q in R.

Z
P
n Q Y
z
n
O y

FIGURE P4.5.1 n x B
R
A body B moving in a reference X
frame R.