Page 331 - Dynamics of Mechanical Systems

0593_C09_fm Page 312 Monday, May 6, 2002 2:50 PM

312 Dynamics of Mechanical Systems

M(Nm)
100

FIGURE P9.2.3 0 t (sec)
Braking moment magnitude. 1.0 2.0

D

r
n
FIGURE P9.3.2
A disk D rolling in a straight line.
P9.3.2: A 4-kg circular disk D with radius r or 0.5 m rolls on a straight line with an angular
speed of ω rad/sec (Figure P9.3.2). Find the linear momentum of D.
P9.3.3: A 3200-lb automobile A traveling at 35 mph collides with the rear of a stopped
automobile B weighing 2800 lb. Following the collision, A and B move together as a unit.
If the momenta of the automobiles are conserved during the collision (that is, the momen-
tum of A just before impact is equal to the combined momenta of A and B just after
impact), find the speed of the vehicles just after impact.

Section 9.4 Angular Momentum
P9.4.1: A 2-kg particle P moving in a Cartesian reference frame R has velocity v given by:

v = 6 n − 3 n + 4 n m sec
x y z

where n , n , and n are unit vectors parallel to the X, Y, and Z coordinate axes of R. If
y
z
x
the coordinates of P are (–1, 5, 4) (in meters), determine the angular momentum of P about
the origin O.
P9.4.2: Repeat Problem P9.4.1 if P weighs 2 lb and if the units of the coordinates and
velocity of P are in feet instead of meters.
P9.4.3: Repeat Problems P9.4.1 and P9.4.2 if the reference point instead of the origin is Q
with coordinates (2, –1, 3).
P9.4.4: A set S of five particles P (i = 1,…, 5) is moving in an inertial reference frame R.
i
Let n , n , and n be mutually perpendicular unit vectors parallel to Cartesian axes X, Y,
z
x
y
and Z fixed in R. Let the P have masses (m ), coordinates (x , y , z ), and velocity components
i
i
i
i
i
(v , v , v for n , n , n ) as listed in Table P9.4.4, where the masses are in kilograms, the
iy
ix
iz
z
y
x
coordinates are in meters, and the velocity components are in meters per second. Find the
angular momentum of S about the origin O.
P9.4.5: See Problem P9.4.4. Let G be the mass center of S. Find the coordinates of G.