ENME 221 Engineering Dynamics
Instructor: Dr. Dave Irvine
Discussion Leaders:
Aakash Bajpai M 11-11:50 (ITE 233)
Matthew Bleakney F
9-9:50
(SHER 013)
Daniel Conlon
F 11-11:50
(SHER 013)
Grader:
12.2Rectilinear Kinematics Continuous
Kinematic variables
A smooth cylinder (m) is supported by a
spring (k). Determine the velocity v of
the cylinder when it moves down s from
its equilibrium position, caused by the
application of force F.
[m = 4 kg, k = 120 N/m, s = 0.2 m, F =
60 N]
cfw_ v = 2.19 m/s
If arm OA
Todays Two-part Agenda:
1. A system of particles (13.3 &
14.3)
2. Conservative forces and
Conservation of Energy
Newtons law for a system of
particles
half the battle is nomenclature!
Consider a particular particle i,
which is one of n particles that
we d
Newtons Law in
Natural Coordinates
F = m (atut + anun +
abub)
Ft = mat = m
Fn = man = mv2/
Fb = 0
Newtons Law in
Cylindrical
Coordinates
F = m (arur + au +
azuz)
Fr = mar = m( r2)
F = ma= m(r + 2)
The tangent to a
curve given in polar
coordinates
in othe
Linear and angular momentum
The principle of impulse and momentum
L= I
where I = F dt
L = mvG
H o = Mo
where MO = Mo dt
HO = (rG/O x mvG) + IG
or HO = (rG/O x mvG)k + IG
Conservation of linear and angular momentum
L= 0
where L = mvG
Ho = 0
where HO = (r
Mass moment of
This week,inertia
we begin the last major element
of rigid body dynamics: Newtons law. The
first step is to briefly review mass moment of
inertia.
Consider a rigid body with a
center of
mass at G. It is free to rotate
about the z axis, whic
2 ft
V=15 ft/s
O
A
If the disk is moving with a
velocity
at point O of 15 ft/s and
s
s
F
ds
=
Ft ds the velocity
s 2 t rad/s, determine
s
at
A.
s
s
2
2
1
2
1
Fn ds
Fn ds
A) 0 ft/sB) 4 ft/s
s1
2
s1
C) 15 ft/s D) 11 ft/s
2 ft
V=15 ft/s
O
A
If the
disk i
If a rigid body is in translation only,
the velocity at points A and B on the
rigid body _ .
A) are usually different
B) are always the same
C) depend on their position
D) depend on their relative position
A Frisbee is thrown and curves to the
right. It i
Mass moment of inertia is a measure of the resistance of a
body to _.
A) translational motion B) deformation
C) angular acceleration D) impulsive motion
s2
s1
s2
s1
Ft ds
Fn ds
s2
Ft ds
s1
s2
Fn ds
s1
Mass moment of inertia is always _.
A) a negative qu
Kinetic energy due to the rotation of a body is defined as
A) (1/2) m (vG)2.
B) (1/2) m (vG)2 + (1/2) IG 2.
C) (1/2) IG 2.
D) IG 2.
s2
s1
s2
s1
Ft ds
Fn ds
s2
Ft ds
s1
s2
Fn ds
s1
2. A slender bar of mass m and length L is released from rest in
a horizo
The second corollary of
Newtons law
1. Principle of linear impulse
and momentum
2. Conservation of momentum
The time integral of Newtons law
F = ma = =
where, by a standard convention, L = mv
Deriving the Principle of Linear Impulse and
Momentum couldnt
Work and
We now have: FEnergy
= ma = m
Consider only the case of fixed mass: F =
First, integrate this along the particles path,
.
We get U12 = T2 T1 = T, where the work
done on the particle from point 1 to point 2
along the path is U12, the kinetic ener
Determine the moment of inertia about an axis
perpendicular to the page and passing through the pin
at O. The think plate has a hole in its center. Its
thickness is 50mm, and the material has a density
= 50 kg/m3.[IO = 6.23 kgm2]
The trailer with its loa
The relationship of torque
(or applied moment)
to angular momentum
1. Application of Newtons law
2. The momentum/impulse integral for
angular momentum
3. Conservation of angular momentum
Angular momentum
Ho = r mv =
i
rx
mvx
j
k
ry
rz
mvy mvz
The magnitud
The Work-Energy relation for a planar rigid body
T1 + U12 = T2
The only change is that T now includes the kinetic
energy of the rigid bodys rotation about its center of
mass as well as the motion of its mass center.
T = mvG2 + IG 2
(Ill give you a plausib
Relative motion the general (planar) case
Our last look at rigid body kinematics is not really
about rigid body kinematics, but a useful technique
for the solution of such problems. And that technique
uses an equation very much like the equations weve
alr
The hook is attached to a cord wound around
a drum. If it moves from rest with an
acceleration of 20 ft/s2, determine the angular
acceleration of the drum and its angular
velocity after the drum has completed 10
revolutions. How many more revs will the
dr
University of Maryland, Baltimore County
Department of Mechanical Engineering
Fall 2016
ENME 303 - Topics in Engineering Mathematics
Homework 9
Maria C Sanchez
For the first three problems submit a word document that contains for each problem: a
copy of a
University of Maryland, Baltimore County
Department of Mechanical Engineering
Fall 2016
ENME 303 - Topics in Engineering Mathematics
Maria C Sanchez
Homework 7: Due Monday, October 31, 2016 by midnight
The following system of equations was generated by ap
University of Maryland, Baltimore County
Department of Mechanical Engineering
Fall 2016
ENME 303 - Topics in Engineering Mathematics
Maria C Sanchez
Homework 10 Due December 2, 2016 by midnight
Submit a word document that contains for each problem: a copy
CALIFORNIA STATE UNIVERSITY FRESNO
Department of Mechanical Engineering
Fall 2016
ENME 303 - Topics in Engineering Mathematics
Maria C Sanchez
Homework 5: Due October 7, 2016
Submit a word document that contains for each problem: a copy of any script and