DYNAMICS OF RIGID BODIES
I N T R OD U C T I ON TO D Y N A M I C S
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CLASSICAL DYNAMICS
The study of motion
of bodies using the
principles
established by
Newton and Euler.
Absolute Motion
Kinematics
Particles
Relative Motion
Rigid Bodies
Force - Mass Acceleration Method
Classical
Dynamics
Kinetics
Work – Energy
Method
Impulse – Momentum
Method
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CONCEPTS & DEFINITION
Engineering Mechanics deals with the effect of forces on objects.
These are the mechanic principles used in vibration, spacecraft
design, fluid flow, electrical, mechanical design etc.
Statics deals with effect of force on bodies which are not moving
Dynamics deals with force effect on moving bodies
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CONCEPTS & DEFINITION
Particle is a mass point; it possesses a mass but has no size; it is an
approximate model of a body whose dimensions are negligible
Rigid Body is a definite amount of matter, the parts of which are fixed
in position relative to each other; non-deformable
Force is that which changes or tends to change the state of motion of
a body or a particle; this applies to the external effect of a force
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MAIN BRANCHES OF DYNAMICS
Kinematics is the study of the geometry of motion, used to relate
displacement, velocity, acceleration, and time; but is not concerned
to the cause of the motion
Kinetics deals with the relationships between the forces acting on the
body, the mass of the body, and the motion of the body
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DISPLACEMENT, VELOCITY and
ACCELERATION OF A PARTICLE
DISPLACEMENT
change of position, expressed as
Δs = s’ – s
where: Δs – positive if the particle’s final position is to the right of the initial
position, and negative if to the other
VELOCITY
the vector counterpart of speed, expressed as
Δs ds
V = Δt = dt
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DISPLACEMENT, VELOCITY and
ACCELERATION OF A PARTICLE
ACCELERATION
the change of velocity at an interval of time, expressed as
Δv dv d2s
a = Δt = dt = dt2
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SAMPLE PROBLEM #1
The car moves in a straight line for a short time. Its velocity is defined
by the equation,
v = (3t2 + 2t) ft/sec
where t is in seconds. Determine its position and acceleration when t
= 3 seconds. NOTE. At t = 0 seconds, s = 0.
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SAMPLE PROBLEM #2
A racket moves along a straight track according to the equation,
s = 3t3 + t + 2
where s is in ft., and t is in seconds.
(a) determine the displacement, velocity, and acc. at t = 4secs
(b) what is the average acceleration during the 5th second
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SAMPLE PROBLEM #3
A particle moves along a horizontal path with a velocity of ,
v = (3t2 - 6t) m/sec
If it is initially located at the origin O, determine the distance
travelled in 3.5 seconds and; the particle’s average velocity and
average speed during the time interval of t = 0 to t = 3.50 seconds.
NOTE. The velocity is negative when 0 ≤ t ≤ 2seconds and positive
when t > 2seconds.
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CHARACTERISTICS OF TRANSLATION
Translation defined as the motion of the rigid body in which
a straight line passing through any two of its particles always
remains parallel to its initial position.
Rectilinear. The motion of a translating body moving in a straight line.
Curvilinear. The motion of a translating body moving in a curve line.
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CHARACTERISTICS OF TRANSLATION
Give the formulas, including the derivations.
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SAMPLE PROBLEM #4
An object starts from rest, moves in a straight line with a constant
acceleration and covers the distance of 64 meters in 4 seconds.
Calculate the following:
(a) acceleration
(b) final velocity, Vf
(c) time the object had covered half the total distance, 64 m
(d) distance the object had covered in half the total time, 4secs
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SAMPLE PROBLEM #5
A racing car has an initial velocity of 100 m/sec and covers a distance
of 725 m in 10 seconds. Find the following:
(a) acceleration
(b) final velocity, Vf
(c) if within 10 seconds, it stopped, what is the sudden
acceleration of the car
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SAMPLE PROBLEM #6
A car starts at 10 m/s and accelerates at 1 m/sec2 in 10 seconds, solve
for the following:
(a) final velocity, Vf
(b) the total distance the car covered
FEU - INSTITUTE OF TECHNOLOGY - CIVIL ENGINEERING DEPARTMENT
SAMPLE PROBLEM #7
A car moving at 30 m/s slows uniformly to a speed of 10 m/s in a time
of 5 seconds. Determine the following:
(a) acceleration of the car
(b) distance it moves in the third second
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SEATWORK – V E R T I C A L M OT I ON
A ball is tossed with a velocity of 10 m/s directed vertically upward
from a window located 20 m above the ground. Determine:
(a) velocity equation, Vf, of the ball at any time, t
(b) elevation equation, y, of the ball above the ground at any time, t
(c) the highest elevation reached by the ball above ground (m)
(d) time the ball will hit the ground (sec)
(e) velocity of the ball when it hit the ground (m/sec)
FEU - INSTITUTE OF TECHNOLOGY - CIVIL ENGINEERING DEPARTMENT
SAMPLE PROBLEM #8
A stone is thrown vertically upward and returns to the earth in 10
seconds. What was its initial velocity and how high did it go?
FEU - INSTITUTE OF TECHNOLOGY - CIVIL ENGINEERING DEPARTMENT
SAMPLE PROBLEM #9
A boy tosses a coin upward with a velocity of 14.7 m/s. Find the
following:
(a) the maximum height reached by the coin from the boy’s hand
(b) the time of flight until the coin returns to the hand
(c) velocity when the coin returns to the hand
(c) Suppose the boy failed to catch the coin, and the coin goes to the
ground, with what velocity will it strike the ground? (the boy’s
hand is 0.49 m above the ground)
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