Page 295 - Dynamics of Mechanical Systems

0593_C08_fm Page 276 Monday, May 6, 2002 2:45 PM

276 Dynamics of Mechanical Systems

O
n ⊥
30°

FIGURE P8.9.2 n
A rod held at 30° before release from rest.
P8.9.3: See Problem P8.9.2. Let n and n be unit vectors parallel and perpendicular to B

⊥
as in Figure P8.9.2. Find the n and n components of the reaction force at O. Specifically,

⊥
observe that O is not zero. Compare these results with similar results for a simple

pendulum.
P8.9.4: Consider a pendulum consisting of a rod B with length and mass m and a thin,
circular disk D with radius r and mass m, as in Figure P8.9.4. Let B and D be rigidly
attached to each other. Find the governing equation of motion, analogous to Eq. (8.9.10).
O

θ
B
D
r
FIGURE P8.9.4
A rod/disk pendulum.

Section 8.10 Double-Rod Pendulum

P8.10.1: Consider a double-rod pendulum as in Section 8.10, with a concentrated mass m
at the lower end of the second bar. Develop governing equations analogous to Eqs. (8.10.12)
and (8.10.13).

Section 8.12 A Rotating Pinned Rod
P 8.12.1: Consider a rotating shaft S with a rod B affixed (that is, welded or otherwise
bonded) to the surface of S with B inclined at an angle θ to the axis of S as in Figure
P8.12.1. Let n , n , and n be mutually perpendicular unit vectors parallel to principal axes
2
3
1
of B such that n is along B, n is perpendicular to B and parallel to a radial line of S which
3
1
passes through the attachment O of B to S, and n is perpendicular to n and n . Finally,
1
3
2
Ω
O n 3
n
2
S θ B
n
FIGURE P8.12.1 1
A rotating shaft S and a rod B bonded to the
surface of S.