Page 429 - Dynamics of Mechanical Systems

0593_C11_fm Page 410 Monday, May 6, 2002 2:59 PM

410 Dynamics of Mechanical Systems

P11.9.2: A rod B with length and mass m is pinned to a vertical rotating shaft S as
depicted in Figure P11.9.2. Let the pin axis be along a radial line of S. Let θ define the
angle between B and S. Let the rotation speed of S be specified as Ω. This system has one
degree of freedom represented by the angle θ. Determine the generalized inertia force F θ * ,
assuming the shaft radius r is small.

θ

S B
θ
S B

Ω
φ

FIGURE P11.9.2 FIGURE P11.9.4
A rod B pinned to a rotating shaft S. A rod B pinned to a rotating shaft S.
P11.9.3: Repeat Problem P11.9.2 by not assuming a small shaft radius; that is, include the
effect of the shaft radius in the analysis.
P11.9.4: See Problem P11.9.2. Suppose the rotation of S is not specified but instead is free,
or arbitrary, and defined by the angle φ as in Figure P11.9.4. This system now has two
degrees of freedom, represented by the angles θ and φ. Determine the generalized inertia
forces F θ * and F φ * , assuming the shaft radius r is small.
P11.9.5: Repeat Problem P11.9.4 by not assuming the shaft radius is small; that is, include
the effect of the shaft radius in the analysis and in this regard, let the mass of S be M.
P11.9.6: See Problem P11.6.6. Consider again the rotating tube with a particle P of Problem
P11.6.6 and as shown again in Figure P11.9.6. Letting the rotating speed Ω be constant as
before, and, letting the mass of P be m, determine the generalized inertia force for the
angle θ, F θ * .

Ω

T

r
θ
P(m)

FIGURE P11.9.6 FIGURE P11.9.7
A particle moving inside a smooth-surfaced tube. A cone rolling on an inclined plane.
P11.9.7: See Problem P11.6.7. Consider again the cone rolling on an inclined plane of
Problem P11.6.7 and as shown again in Figure P11.9.7. As determined in Problem P11.6.7,