Statics & Strengt
th of Materials (MAT
TR71025) Centroid and Cen
ntre of Gra
avity
710 5
MA R7 025
MATR
Sta ics
ati
(C ntr d)
Cen roid
In
nstruct Moham
tor: M
mmad T
Tooran
ni
Statics (M
MToorani)
P
Page 1
Statics & Strength of Materials (MATR71025) C

x-v-a-t Graphs
Position Velocity Acceleration Time Graphs
Physics - Mechanical (x-v-a-t Graphs)
1
s-t (Position-Time) GRAPH
Plots of position vs. time can be
used to find velocity vs. time
curves. Finding the slope of the
line tangent to the motion curve

CURVILINEAR MOTION: CYLINDRICAL COMPONENTS
Todays Objectives:
Students will be able to:
1. Determine velocity and
acceleration components
using cylindrical
coordinates.
In-Class Activities:
Check Homework
Reading Quiz
Applications
Velocity Components

Mechanisms
What is a Mechanism?
A mechanism is the part of a machine
which contains two or more pieces
arranged so that the motion of one
compels the motion of the others.
Generally used to:
Change the direction of movement
Change the type of movement

Center of Gravity and Mass Moment of Inertia of Homogeneous Solids
z
z
r
V = 4 r 3
3
r
V = r 2h
G
h
2
G
y
x
x
Sphere
Ixx = Iyy = Izz = 2 mr 2
5
Cylinder
Ixx = Iyy =
1
12
1
m(3r2 + h2) Izz = mr2
2
z
z
V = 1 r 2h
3
V = 2 r 3
3
y
h
2
G
r
h
4
G
h
y
y
r
3r
8
x

Description Figure Momenﬂs} of inertia
Point mass m at a distance rfrorn the axis F}
of rotation. I: m
Two point masses, M and m, with reduced Mm 2 2
- I = —:r, 2 #1:
mass ,u and separated by a distance, x. fvf+m
Rod oflength i. and mass m I TEL? [11
(Axi

PHYS-71090 & PHYS-1152 Assignment [MOI] Fall 2013
Q1.
Determine the coordinates of the mass center of the body constructed of steel
plate and a steel rod. The plate thickness is 2 mm. The rod diameter is 4 mm and
its length is 50 mm. The origin O is at th

PHYS-71095 and PHYS-1152
Assignment No. 8 Fall 2014
Q1.
Determine the moments of inertia Ix and Iy of the area shown with respect to
centroidal axes respectively parallel and perpendicular to side AB.
Q2.
A square hole is centered in and extends through t

Geometric Properties of Line and Area Elements
Centroid Location
y
r
Centroid Location
y
L = 2 r
C
Area Moment of Inertia
A = r2
r
C
x
r sin
Ix = 1 r 4 ( 1 sin 2)
4
2
x
Iy = 1 r 4 ( + 1 sin 2 )
4
2
r sin
2
3
Circular sector area
Circular arc segment
y

ABSOLUTE DEPENDENT MOTION ANALYSIS OF
TWO PARTICLES
Todays Objectives:
Students will be able to:
1. Relate the positions, velocities,
and accelerations of particles
undergoing dependent motion.
In-Class Activities:
Check Homework
Reading Quiz
Applicati

CURVILINEAR MOTION:
NORMAL AND TANGENTIAL COMPONENTS
Todays Objectives:
Students will be able to:
1. Determine the normal and
tangential components of
velocity and acceleration of a
particle traveling along a
curved path.
In-Class Activities:
Check Homew

MOTION OF A PROJECTILE
Todays Objectives:
Students will be able to:
1. Analyze the free-flight
motion of a projectile.
In-Class Activities:
Check Homework
Reading Quiz
Applications
Kinematic Equations for
Projectile Motion
Concept Quiz
Group Problem

RECTILINEAR KINEMATICS: ERRATIC MOTION
Todays Objectives:
Students will be able to:
1. Determine position,
velocity, and acceleration of
a particle using graphs.
In-Class Activities:
Check Homework
Reading Quiz
Applications
s-t, v-t, a-t, v-s, and a-s

CURVILINEAR MOTION:
GENERAL & RECTANGULAR COMPONENTS
Todays Objectives:
Students will be able to:
1. Describe the motion of a
particle traveling along a
curved path.
2. Relate kinematic quantities
in terms of the rectangular
components of the vectors.
In-

INTRODUCTION &
RECTILINEAR KINEMATICS: CONTINUOUS MOTION
Todays Objectives:
Students will be able to:
1. Find the kinematic quantities
(position, displacement, velocity,
and acceleration) of a particle
traveling along a straight path.
In-Class Activities:

Find the equation of motion for the illustrated car model. The axles are massless. Assume that
all motion occurs in the x direction and that the car rolls without slip.
Shown is a simple vehicle, consisting of a driven wheel W (treat it as a uniform cylin