Determination of the Motion of a Particle
If Acceleration is given
- as a function of time: a = f(t)
- as a function of position: a = f(x)
- as a function of velocity: a = f(v)
How to obtain the motion
of the particle, x(t) ?
47
Determination of the Moti

14:440:222 Dynamics
(Lecture Note #14)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Planar rigid body motion: translation
and rotation
Absolute motion analysis
Applications
Does each passenger
experience the same
velocity and accelerati

14:440:222 Dynamics
(Lecture Note #15)
Instructor: Prof. Peng Song
Rutgers University
Applications
As the slider block A moves horizontally to the left with vA, it causes
the link CB to rotate counterclockwise. Thus vB is directed tangent to
its circular

14:440:222 Dynamics
(Lecture Note #16)
Instructor: Prof. Peng Song
Rutgers University
Applications: IC of Zero Velocity
The instantaneous center (IC)
of zero velocity for this bicycle
wheel is at the point in contact
with ground. The velocity
direction at

14:440:222 Dynamics
(Lecture Note #17)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Relative motion analysis: acceleration
Applications
In the mechanism for a window, link
AC rotates about a fixed axis through
C, and AB undergoes general

14:440:222 Dynamics
(Lecture Note #18)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Relative-Motion Analysis Using Rotating
Axes
Relative Motion Analysis: Velocity
The velocity at B is given as :
or
(drB/dt) = (drA/dt) + (drB/A/dt)
vB =

14:440:222 Dynamics
(Lecture Note #19)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Mass moment of inertia
Applications
The large flywheel in the picture is
connected to a large metal cutter. The
flywheel mass is used to help provide a
u

14:440:222 Dynamics
(Lecture Note #20)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Planar kinetics of rigid body:
Translational and fixed-axis rotational
motion
Applications
The boat and trailer undergo
rectilinear motion. In order to
f

14:440:222 Dynamics
(Lecture Note #21)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Planar kinetics of rigid body: General
planar motion
Applications
As the soil compactor accelerates
forward, the front roller experiences
general plane m

14:440:222 Dynamics
(Lecture Note #22)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Work and energy for rigid body motion
Applications
The work of the torque (or moment) developed by the driving
gears on the two motors on the concrete mi

Example 4
Given: A linkage undergoing motion as shown. The velocity of the block, vD, is 3 m/s. Find: The angular velocities of links AB and BD. Plan: Locate the instantaneous center of zero velocity of link BD and then solve for the angular velocities.
E

14:440:222 Dynamics
(Lecture Note #13)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Angular impulse and angular momentum
Application
Planets and most satellites move in elliptical orbits. This motion
is caused by gravitational attraction

14:440:222 Dynamics
(Lecture Note #12)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Impact
Applications
The quality of a tennis ball is measured by the height of its
bounce. This can be quantified by the coefficient of
restitution of the

14:440:222 Dynamics
(Lecture Note #11)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Linear impulse
Linear momentum
Linear Impulse: Applications
When a stake is struck by a
sledgehammer, a large impulse force
is delivered to the stake an

14:440:222 Dynamics
(Lecture Note #2)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Curvilinear motion
Rectangular coordinates
Applications
The path of motion of a plane
can be tracked with radar and
its x, y, and z coordinates
(relative

14:440:222 Dynamics
(Lecture Note #3)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Curvilinear motion
Normal-tangential (n-t) coordinates
Applications
Cars traveling along a clover-leaf
interchange experience an
acceleration due to a ch

14:440:222 Dynamics
(Lecture Note #4)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Curvilinear motion
Polar Coordinates
Cylindrical coordinates
Applications
Cylindrical Components
We can express the location of P in polar coordinates a

14:440:222 Dynamics
(Lecture Note #5)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Kinematic Analysis of Two-Particle Systems
Dependent motion
Relative motion
Applications
The cable and pulley system shown
can be used to modify the spee

14:440:222 Dynamics
(Lecture Note #6)
Instructor: Prof. Peng Song
Rutgers University
Solution to Example 4 from Lecture Note #5
Given:
Find:
vA = 30 mi/h
vB = 20 mi/h
aB = 1200 mi/h2
aA = 0 mi/h2
vB/A
aB/A
Plan: Write the velocity and acceleration vectors

14:440:222 Dynamics
(Lecture Note #7)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Kinetics of particle systems in n-t
coordinates
Applications
Normal-Tangential Coordinates
When a particle moves along a
curved path, it may be more
conve

14:440:222 Dynamics
(Lecture Note #8)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Kinetics of particle systems in polar
and cylindrical coordinates
Applications
Cylindrical Coordinates
Equations of Motion in cylindrical coordinates (usi

14:440:222 Dynamics
(Lecture Note #9)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Work and energy
Applications
A roller coaster makes use of gravitational forces to assist the
cars in reaching high speeds in the valleys of the track.
Ho

14:440:222 Dynamics
(Lecture Note #10)
Instructor: Prof. Peng Song
Rutgers University
Todays Lecture
Power and efficiency
Conservative forces and conservation of
energy
Power and Efficiency: Applications
Engines and motors are often rated
in terms of th

14:440:222 Dynamics
(Lecture Note #23)
Instructor: Prof. Peng Song Rutgers University
Today's Lecture Conservation of energy
Applications
The torsion springs located at the top of the garage door wind up as the door is lowered. When the door is raised, th