1. The lunar module descends to the moons surface under retrothrust. At
a height of 5 meters, it is traveling at 2 m/sec downward. At this point, the
engines are cut off abruptly and the vehicle falls freely to the surface. If the
lunar acceleration due t

Problem 16-4 (Page 323)
The disk below is rotating at to“ = 8 rad/sec about a ﬁxed axis. If it is sub—
JCCtEd to a constant angular acceleration of a 6 rad/secz, determine a) the
magnitudes of the velocity and b) the n and t components of acceleration
ofp

Problem 17—20 (Page 408) I
The pendulum shown'consists of two slender rods AB and 0C, each
with a mass per length of 3 kg/m. The thin circular plate, which has a
Small hole in the center, has amass per area of 12 kg/mz. Determine
the location Y of the mas

Equations of Motion
General Plane Motion of a Rigid Disk
Rolling and Sliding
L,
21Fx = P — F = maG
4121: = N — mg = 0
y
€ZMG = Fr = IGoc
Frictional Rolling:
No Slipping vG = r0)
Slipping: Counterolockwise rotation of a rigid body in the X-y plane
about an

Kinematics of a Rigid Body
Rotation about a fixed axis
General Plane Motion
Motion occurs when an object experiences
both translation and rotation
Curvilinear translation
General plane motion
Rectilinear translation
Rotation about a ﬁxed axis Angular

L As an airplane begins its takeoff run, the normal forces exerted on the tires-
by the runway at A and B are N A = 720 lb and NB = 1600 lb. Determine the
magnitude of the airplane’s acceleration
For fl} F331?
4! 4;
flEﬁC‘A/A+AJIA kw: O
. . rﬁ:
W: 720

45
4.6
Implicitly Satisfying Constraints
As was discussed in Section 3.13, some constraint equations cannot be solved analytically and
used to eliminate dependent generalized coordinates from the model. In this case, the differentiation done to find the v

Homework #6
(279pts)
Due November 3 or 4, 2016
5. (65pts) The solid cylinder has an outer radius R, height h, and is made from a material having a density
that varies from its center as = k + ar2 , where k and a are constants. Determine the mass of the cy

Homework #5
5.7.3
(531pts)
Due October 13 or 14, 2016
Solutions to Practical Exercises
(2pts)
^ ^
Y
Aj
1. (161pts) The wheel in Fig. 5.1 consists of a thin ring having a mass of 10kg and four spokes made
from slender rods and each having a mass of 2kg . T

l. A cord is wrapped around a homogeneous disk of radius r = 0.5 m and has a mass
of m = 15 kg. If the cord is pulled upward with a force of T = 180 N, determine
a) the acceleration of the center of the disk , aC and
b) the angular acceleration of the dis

l. A boat is moving at 10 m/sec when its engine is shut down. Due
to hydrodynamic drag, its subsequent acceleration is a = — 0.05 v2
(m/secz), Where v is the velocity of the boat in m/sec. Determine the
boat’s velocity 4 seconds after the engine shut down

1. Two bodies, A (mA = 15 kg) and B (InB = 10 kg) are connected by a ﬂexible
cable as shown. The kinetic coefficient of friction between body A and the in-
clined surface is “K = 0.2. The horizontal surface supporting B is smooth. When
the bodies are in t

1'. A 2000Ib car starts from rest at point 1 as shown and moves without
friction down the track that has a radius of curvature p2 = 20 ft. Determine
a) the force exerted by the track on the car at point 2, and b) the radius of _
curvature p3 that would ca

1. A 58g tennis ball has a horizontal speed of 10 m/sec when it is struck by
a tennis racket as shown. After the impact, the ball's velocity is 25 m/sec
and makes an angle of 15 with initial direction. if the time of contact is
0.05 sec, determine the a

1. For the linkage shown, the block C is moving downward at 4 ft/sec.
Use the method of Instanteneous Centers (I.C. Method) to determine the
angular velocities of members AB and BC, and the linear velocity (magni—
tude and direction) of a point on member

Homework #4
(662pts)
Due October 6 or 7, 2016
6. (82pts) The platform is rotating about the vertical axis such that at any instant its angular position is
3
= 4t 2 rad, where t is in seconds. A ball rolls outward along the radial groove so that its posit