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0593_C14_fm Page 511 Tuesday, May 7, 2002 6:56 AM

Stability 511

P14.3.2: See Problem P14.3.1. If the tube radius r is 0.5 m, determine the angular speed Ω
so that the particle position θ = 0 is unstable.

Section 14.5 The Rolling/Pivoting Circular Disk
P14.5.1: A uniform circular disk with radius 8 in. is rolling on a straight line on a level,
perfectly rough surface as represented in Figure P14.5.1. Determine the minimum speed
v needed for stability of the motion.

v
FIGURE P14.5.1
A circular disk rolling in a straight
line on a perfectly rough surface.

P14.5.2: Repeat Problem P14.5.1 for a disk with radius 25 cm.
P14.5.3: A uniform circular disk with radius 10 in. is pivoting on a flat horizontal surface
as represented in Figure P14.5.3. Determine the minimum angular speed Ω for stable
rotation.

Ω

FIGURE P14.5.3
A pivoting circular disk.

P14.5.4: Repeat Problem P14.5.3 for a disk with radius 30 cm.
P14.5.5: Consider a ring or hoop with radius r rolling on a perfectly rough horizontal
surface as in Figure 14.5.5. Following the procedures of Section 14.5, develop the governing
dynamical equations analogous to Eqs. (14.5.1), (14.5.2), and (14.5.3).

Z

θ

ψ
G
r φ
X
FIGURE P14.5.5
A rolling ring. Y