Page 294 - Dynamics of Mechanical Systems

0593_C08_fm Page 275 Monday, May 6, 2002 2:45 PM

Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 275

P8.8.3: See Problem P8.8.2. Repeat Problem P8.8.2 using pulley radii of 5 in. and 10 in.,
outer mass weight of 6 lb and inner mass weight of 7 lb, and a pulley weight of 4 lb.
P8.8.4: A 4-kg circular disk D with 15-cm radius is mismounted on a shaft so that its center
O is 5 mm away from the shaft axis A, as in Figure P8.8.4. If the shaft rotates at 300 rpm,
determine the magnitude of the resultant inertia force on D.

D
D
5 mm
O
A A
15 cm
A
B B

FIGURE P8.8.4
A mismounted circular disk.

P8.8.5: A thin, circular disk D with mass m and radius r is mismounted on a shaft S so
that its axis makes a small angle θ with the shaft axis as in Figure P8.8.5. Using Eqs.
(8.6.10), (8.6.11), and (8.6.12) determine the n and N (i = 1, 2, 3) components of the inertia
i
i
torque exerted on D if S rotates at an angular speed Ω. (N is parallel to the axis of S and
3
n is parallel to the axis of D.)
3
θ
D N 1
B S B
θ n
1
N
3
O
n
b b 3
FIGURE P8.8.5 n , N 2
2
A mismounted circular disk.
P8.8.6: See Problem P8.8.5. Evaluate the torque components for the following data: m = 4
kg, r = 15 cm, θ = 5°, and Ω = 300 rpm. Also, if bearings B are supporting S on both sides
of D as in Figure P8.8.5, find the forces on the bearings due to the misalignment angle if
the distance b of the bearings from the center O of D is 20 in.

Section 8.9 The Rod Pendulum

P8.9.1: A 1-m-long rod B with mass 1 kg is supported at one end O by a frictionless pin
and held in a horizontal position as in Figure P8.9.1. If the rod is suddenly released, find
the angular acceleration α of the rod and the horizontal and vertical components of the
reaction force (O and O ) at O at the instant of release.
y
x
1 kg
FIGURE P8.9.1 O 1 m
A rod held in a horizontal position before
release from rest.

P8.9.2: See Problem P8.9.1. Repeat Problem P8.9.1 if B is held at a 30° inclination just before
it is released, as represented in Figure P8.9.1.