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A. Space, Time and Motion
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A. Space, Time and Motion
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A.
Space, Time and Motion
Created
2024/06/24 03:17
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A.1.1 Instantaneous and average
Average Speed :
Entire distance covered divided by the amount of time elapsed since it started
•
the average speed is determined solely by a magnitude which excludes the direction
•
the average speed is a scalar quantity so it uses distance, which is also a scalar, to calculate it
•
the equation of average speed is :
v
ˉ
=
Δ
x
Δ
t
\bar{v}= \frac{\Delta x}{\Delta t}
v
ˉ
=
Δ
t
Δ
x
v
ˉ
=
a
v
e
r
a
g
e
s
p
e
e
d
,
∆
x
=
c
h
a
n
g
e
i
n
d
i
s
t
a
n
c
e
,
∆
t
=
c
h
a
n
g
e
i
n
t
i
m
e
\bar{v}=average\ speed, ∆x=change\ in\ distance, ∆t=change\ in\ time
v
ˉ
=
a
v
er
a
g
e
s
p
ee
d
,
∆
x
=
c
han
g
e
in
d
i
s
t
an
ce
,
∆
t
=
c
han
g
e
in
t
im
e
Instantaneous Velocity
•
Often referred to simply as velocity, is a vector of how quickly an object’s displacement is changing at precisely one specific point somewhere along its route
•
If two points on the path are used to calculate the velocity (separated by a non-zero amount of time), it is instead average velocity
•
the equation of average velocity is :
v
=
x
(
t
2
)
−
x
(
t
2
)
t
2
−
t
1
v = \frac{x(t_{2})-x(t_{2})}{t_{2}-t_{1}}
v
=
t
2
−
t
1
x
(
t
2
)
−
x
(
t
2
)
•
An
instantaneous velocity
at any time interval is determined by using the following equation :
A.1 Kinematics
A.2.1 Newton’s Laws
Force
•
Forces vectors that cause objects to accelerate
•
Objects that experience zero net force, move in a straight line at a constant velocity
•
Bigger forces accelerate objects faster
•
If the same force is applied to two objects of different masses, the object with larger mass will accelerate less than the object of smaller mass
•
Forces are vectors, so if more than one force acts on an object, the forces add up through vector addition.
•
The total sum of the vectors is a vector called the resultant force. The magnitude of the sum of all the force vectors is called net force.
A.2.1-1 Example of normal reaction forces
•
Gravitational forces
F
g
=
m
⋅
g
⋅
h
F_g = m \cdot g \cdot h
F
g
=
m
⋅
g
⋅
h
•
Tension forces
A.2 Forces and Momentum
A.3.1 Work
Work
•
Energy exists in many forms, but most commonly if it is stored energy it is called potential energy and when the energy is in motion of an object it is called kinetic energy.
•
An object at rest can be assumed to have zero kinetic energy, and an object in motion will have kinetic energy higher than zero.
•
Objects that move faster have more kinetic energy.
•
Since forces cause objects to move faster or slower, forces are what causes the energy to increase or decrease.
•
Energy transferred to or from an object via the application of force along a displacement is referred to as
work
.
•
Since work refers to the energy transferred to or from the object it is also defined as the change in energy
•
Work is formally defined as the product of the force and displacement in the same direction as the force.
W
=
F
⋅
s
⋅
c
o
s
θ
W=F\cdot s \cdot cos\theta
W
=
F
⋅
s
⋅
cos
θ
•
Thus a force will only do work if there is a displacement in the same direction as the force
•
If the angle between the force and the displacement is 90 degrees work done is zero
•
A force does negative work if it has a component in the opposite direction as the displacement (angle
•
between 90° and 180°)
A.3 Work, Energy and Power
A.4.1 Rotational motion equations
Definitions of key terminologies
•
Notice that all variables that describe angular motion have similar analogous variables that describe linear motion.
•
All the suvat equations can be rewritten using angular variables
A.4.2 Torque
Torque
•
If all linear variables have a rotational analogue it follows that force used in linear equations will also have a rotational analogue
•
Torque is used the same way in rotational equations and is defined as the product of the tangential force times the distance from the point the force is applied to the center of rotation.
•
Newton’s laws of motion apply to torque the same way they apply to forces
•
Notice that Newton’s second law requires a quantity that is similar to mass, but that can be used in rotational motion equations. This quantity is called moment of inertia and is discussed below.
•
Be careful when calculating the torques since torque values depend on the distance to the center of rotation, rotating (or sometimes called pivoting) about a different axis will result in different values of torque.
A.4 Rigid Body Mechanics
A.5.1 Frames of reference
Frames of reference
•
The concept of position and coordinates requires one to choose an origin point as (0,0)
•
The choice of origin point does not affect any of the behaviour. This means that regardless of origin, displacement and velocity are not affected.
•
A frame of reference performs all calculations using a specific choice of point of origin (0,0), but from another observer’s perspective that point of origin can appear to be moving at a constant velocity.
•
Take for example two people standing on two platforms.
•
Once one chooses a specific frame of reference, all other frames of reference appear to have an initial position and a constant velocity.
•
There is no “correct” frame of reference. The laws of physics work the same way regardless of which frame you choose as long as all measurements are made using the same frame.
•
This is why measurements of velocity and position don’t really make sense unless one also specifies which frame of reference (point of origin) is used to make the measurements of velocity and position.
A.5.2 Galilean relativity
Galilean relativity
•
Galilean relativity makes sure that Newton’s laws of motion apply the same way in all frames of reference.
•
The measurement of time is the same for all frames of reference.
Galilean transformations
A.5 Galilean and Special Relativity
