106 PHYS-CH1-Part1
Review of Trigonometry
For right triangles only!
H
O
sin θ =
H
A
cos θ =
H
O
tan θ =
A
O
θ
A
Pythagorean Theorem
H2 = A2 + O2
SOHCAHTOA
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Scalars and Vectors
Vocabulary:
Scalars are numbers
Examples: 10 meters
75 kilometers/hour
Vectors are numbers with a direction
Example:
10 meters to the right
75 kilometers/hour north
Scalar: 25 meters
Vector: 25 meters north
Scalar: 25 meters
Vector: 25 meters east
More about vectors will be discuss later
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106 PHYS-CH1-Part1
Introduction to Mechanics
What is Mechanics ?
The study of the motion of objects (through Equations), and the
related concepts of force and energy, form the field called
mechanics.
Mechanics
Kinematics
- the description of
how objects move
Dynamic
the link is
a
- deals with force and
why objects move (CH.3)
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Kinematics
Kinematics : the description of how objects move.
Î Kinematics in one dimension : describing an object that moves
along a straight line path, which is one dimensional motion.
Î Kinematics in two dimensions : the description of the motion of
objects that move in paths in two (or three) dimensions.
Dynamics
Dynamics : deals with force and why objects move as they do.
In this part we will solve the following questions :
Î What makes an object at rest begin to move ?
Î What causes a body to accelerate or decelerate ?
Î What is involved when an object moves in a circle ?
We can answer in each case that a FORCE is required.
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Kinematics – Type of Motion
Type of Motion
Translations
a=
a=
dv
dt
vf -vi
Vibrations
Rotations
ac=
t f -ti
a = - ω2 x
v2
r
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Kinematics – Translational Motions
Type of translational motions
Vertical
Slanting
Horizontal
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Kinematics – Terms and Concepts
Some important terms which you must know !
Reference Frames
Displacement
Distance
Speed
Average Velocity
Instantaneous Velocity
Average Acceleration
Instantaneous Acceleration
1. Reference Frames:
Frames
Any measurement of position, distance or speed must be made with
respect to a frame of reference.
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‫أهﻤﻴﺔ وﺟﻬﺔ اﻟﻨﻈﺮ‬
‫إن ﻣﺎ ﻳﻼﺣﻈﻪ آﻞ ﻣﻨﺎ ﻳﻌﺘﻤﺪ ﻋﻠﻰ وﺟﻬﺔ ﻧﻈﺮﻩ‬
‫ﻼ ‪ :‬ﻧﻔﺘﺮض ﻋﺮﺑﺔ ﻗﻄﺎر ﺗﺴﻴﺮ ﺑﺴﺮﻋﺔ ﺛﺎﺑﺘﺔ ﻣﻘﺪارهﺎ ‪ 30 m/s‬ﻓﻲ إﺗﺠﺎﻩ اﻟﺸﻤﺎل وﺑﺪاﺧﻞ هﺬﻩ اﻟﻌﺮﺑﺔ رﺟﻞ ﻳﻘﺬف آﺮة ﺑﺴﺮﻋﺔ‬
‫ﻓﻤﺜ ً‬
‫ﺛﺎﺑﺘﺔ ﻣﻘﺪارهﺎ ‪ 1 m/s‬ﻓﻲ إﺗﺠﺎﻩ اﻟﺸﻤﺎل‪ ،‬ﻣﺎهﻲ ﺳﺮﻋﺔ اﻟﻜﺮة ؟‬
‫اﻹﺟﺎﺑﺔ ﻋﻠﻰ هﺬا اﻟﺴﺆال ﻗﺪ ﺗﻜﻮن ﺳﻬﻠﺔ وﻟﻜﻦ ﻟﻴﺲ هﻨﺎك إﺟﺎﺑﺔ واﺣﺪة ‪ ......‬آﻴﻒ؟‬
‫اﻹﺟﺎﺑﺔ اﻟﺼﺤﻴﺤﺔ ﺗﻌﺘﻤﺪ ﻋﻠﻰ ﻣﺮﺟﻊ ﻣﻌﻴﻦ أو راﺻﺪ‪ .....‬ﻓﻬﻨﺎك إﺟﺎﺑﺘﻴﻦ‪:‬‬
‫‪ -1‬ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ أرﺿﻴﺔ اﻟﻌﺮﺑﺔ )اﻟﺮﺟﻞ داﺧﻞ اﻟﻌﺮﺑﺔ( ﺗﻜﻮن ﺳﺮﻋﺔ اﻟﻜﺮة ﻣﺴﺎوﻳﺔ ﻟــ ‪ 1 m/s‬ﺷﻤﺎ ًﻻ‬
‫‪ -2‬ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ راﺻﺪ ﻳﻘﻒ ﻋﻠﻰ اﻷرض ﺧﺎرج اﻟﻌﺮﺑﺔ ﺗﻜﻮن ﺳﺮﻋﺔ اﻟﻜﺮة ﻣﺴــــــﺎوﻳﺔ ‪ 1 m/s‬ﺷﻤﺎﻻ ‪ 3 m/s +‬ﺷﻤﺎﻻ أو ‪4 m/s‬‬
‫ﺑﺈﺗﺠﺎﻩ اﻟﺸﻤﺎل‬
‫د‪.‬ﻋﺒﺪﷲ ﻣﺤﻤﺪ اﻟﺰﻳﺮ‬
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106 PHYS-CH1-Part1
Reference Frames, Coordinate Systems
• Every measurement must be made with respect to a reference
frame.
• Usually, speed is relative to the Earth.
• When specifying speed, always specify the frame of reference
unless its obvious (“with respect to the Earth”).
• Distances are also measured in a reference frame.
• When specifying speed or distance, we also need to specify
DIRECTION.
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Coordinate Axes
• Define reference frame using a standard coordinate axes.
• 2 Dimensions (x,y)
+y
• Note, if its convenient,
could reverse + & - !
- ,+
+ ,+
-x
• 3 Dimensions (x,y,z)
+x
+,-
- ,-y
z
y
x
• Define direction using these.
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• For inclined plane problems (later), tilted axes will be used (for
convenience!):
y
x
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2. Distance and Displacement:
Distance:
The length of the actual path or total path length
Example,
Jeddah is ∼1000 km away from Arriyadh.
Displacement:
The change in position of the object.
Δx = xf - xi, Δx means the change in x (position) which is the
displacement.
A vector quantity
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Distance Vs Displacement
Example:
A person walking 70 m to the east and then turning around and
walking back (west) a distance of 30 m.
y
70m
distance
West
x, East
displacement
40m
30m
Total distance = 100 m
Displacement = xf - xi = 70 m - 30 m = 40 m
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3. Average Speed:
Average Speed is defined as the distance travelled along its path divided
by the time it takes to travel this distance,
average speed =
distance travelled
time elapsed
It is a scalar quantity, with unit (ms-1)
4. Average Velocity
Average velocity is defined as the displacement divided by the elapsed
time
average velocity v =
displaceme nt Δx x f - x i
=
=
time elapsed Δt
t f - ti
It is a vector quantity, with unit (ms-1)
READ EXAMPLES 1.3 to 1.8 in the Textbook
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5. Instantaneous Velocity:
The instantaneous velocity is the velocity at any instant of time.
In general the instantaneous velocity at any moment is defined as
the average velocity over an infinitesimally short time interval.
Δ x dx
=
Δt → 0 Δ t
dt
v = lim
READ EXAMPLES 1.9 & 1.10 in the Textbook
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Example:
Example: Velocity
Velocity
Assume
Assume the
the earth
earth is
is in
in circular
circular orbit
orbit about
about the
the sun,
sun, moving
moving at
at aa
constant
constant speed.
speed. What
What are
are the
the earth’s
earth’s
i)i)
average
average velocity
velocity
ii)
ii) average
average speed
speed
iii)
iii) instantaneous
instantaneous velocity
velocity ??
11m
Given
m
Given that
that the
the radius
radius of
of the
the earth’s
earth’s orbit
orbit is
is 1.5X10
1.5X1011
Solution:
i) average velocity
v=
=
displacement Δx x f - x i
=
=
time elapsed Δt
t f - ti
0
= 0 ms − 1
T
because, in one full cycle, the displacement of earth from
original point is zero (earth reaches the initial point again)
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ii) Average speed
vs =
distance travelled
time elapsed
but, d = 2π r = 2π (1.5 × 10 11 m ) = 9.4 × 10 11 m
9.4 × 10 11 m
vs =
= 2.98 × 10 4 ms − 1
(365.25 )( 24 )( 60 )( 60 )
iii) Instantaneous velocity
Because the earth are orbit around the sun at constant speed,
and the average speed is given in (ii) above,
thus,
magnitude of v :
2.98 × 104 ms-1
direction :
tangent to the path at each instant.
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106 PHYS-CH1-Part1
6. Average Acceleration:
Acceleration
Acceleration specifies how rapidly the velocity of an object is
changing. Average acceleration is defined as the change in velocity
divided by the time taken to make this change
average acceleration a =
change of velocity Δ v v f - v i
=
=
Δ t t f - ti
time elapsed
7. Instantaneous Acceleration:
The instantaneous acceleration is the acceleration at any instant of
time. In general the instantaneous acceleration at any moment is
defined as the average acceleration over an infinitesimally short
time interval
instantane ous acceleration a = lim
Δt → 0
Δ v dv
=
Δ t dt
READ EXAMPLES 1.12 to 1.15 in the Textbook
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Conceptual Question #1
• Velocity and acceleration are both vectors (they have magnitude
& direction).
• Are the velocity and the acceleration always in the same
direction?
NO!!•
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