Page 333 - Dynamics of Mechanical Systems

0593_C09_fm Page 314 Monday, May 6, 2002 2:50 PM

314 Dynamics of Mechanical Systems

P9.4.11: A wheel W modeled as a thin circular disk with radius r and mass m rolls on a
straight line as in Figure P9.4.11. If the center G has a speed V, find the angular momentum
of (a) W about G, and (b) W about C.

G
r V
FIGURE P9.4.11 C
Wheel rolling in a straight line.
P9.4.12: Repeat Problem P9.4.11 if the wheel is not a disk but instead is characterized by
an axial radius of gyration k. Let the radius and mass still be r and m.
P9.4.13: A wheel W modeled as a thin, circular disk with radius r and mass m rolls on a
circle with radius R. Let W remain vertical during the motion so that its center G also
moves on a circle with radius R. Determine the angular momentum of (a) W about G, and
(b) W about its contact point C. Express the results in terms of an axial unit vector i and
a vertical unit vector k.
P9.4.14: Repeat Problem P9.4.13 if the wheel is not a disk but instead is characterized by
an axial radius of gyration k and a diametral radius of gyration k . Let the radius and
z
x
mass still be r and m.

Section 9.5 Principle of Linear Impulse and Momentum
P9.5.1: A car traveling at 30 mph is brought to a skid stop on a level asphalt roadway with
all four wheels locked. If the car weighs 3000 lb and if the coefficient of friction between
the tires and the roadway is 0.75, determine the time t required for the car to skid to a stop.
P9.5.2: A 2850-lb test automobile is driven into a fixed, rigid barrier at 35 mph. Determine
the impulse I exerted on the car by the barrier, assuming negligible rebound velocity.
P9.5.3: See Problem P9.5.2. Suppose the automobile in Problem P9.5.2 is stopped in 65 msec
(0.065 sec). Determine the average impulsive force F.
P9.5.4: A 3-kg body B has a velocity 6n – 3n + 4n m/sec in a Cartesian reference frame
z
x
y
R where n , n , and n are unit vectors parallel to the X-, Y-, and Z-axes. A force F, expressed
x
z
y
2
as –18tn + 9(t – t)n – 4t n N, is applied to B. Determine the velocity of B when time t is
3
x
y
z
(a) 0.5 sec, (b) 1.0 sec, and (c) 1.5 sec.
Section 9.6 Principle of Angular Impulse and Momentum
P9.6.1: A drum brake acting on a rotor creates a moment M on the rotor as in Figure P9.6.1.
Let the rotor have an axial moment of inertia of 4 kg m and an angular speed of 420 rpm.
2
Determine the speed reduction after (a) 0.05 sec, (b) 0.1 sec, and (c) 02 sec. Determine the
time to bring the rotor to rest.
P9.6.2: A 20-lb body B has principal radii of gyration given by k = 8 in., k = 4 in., and k z
x
y
= 4 in. Let B have an angular velocity of 20n – 30n + 40n rad/sec, where n , n , and n z
y
y
x
z
x
are principal unit vectors of B for its mass center G. Let a moment be applied to B about
3
2
G given by tn – 3t n – 4(t – t )n ft lb. Determine the angular velocity of B when t is
y
x
z
(a) 0.5 sec, (b) 1.0 sec, and (c) 1.5 sec.