LEARNIT RAMIDORLEAF FLETRAMIDORLEAFLETRAMIDORLEAFLET MIDORLEAFLETRAMIDORLEAFLETRAMIDORLEAFLETRAMID (+63)XXX XXX XXXX (+63)XXX XXX XXXX WWW.LEAFLETS.COM.PH CONTACT PERSON 1 CONTACT PERSON 2 @leafletsph D O N ' T M I S S O IT! YOUWILL G E N E R A L P H Y S I C S 1
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Units, Physical Quantities, and Measurement Vectors and Addition of Vectors Kinematics: Motion Along a Straight Line Average and Instantaneous Acceleration Circular and Projectile Motion Newton's Laws of Motion LEARNIT.WEGOTIT.YOUWILLFORMULOVEIT. 01 02 03 Equations that are easy to memorize. To have a lot of fun while studying. To familiarize yourself with physics more easily. WHAT THIS LEAFLET OFFERS YOU? Center of Mass, Impulse, and Momentum Rotational Motion Gravity Periodic Motion WHAT TO DISCOVER?
bePHYSICS-ALLY ready! opportunities are waiting and so our brochure! Learn how to solve? Problem solved! openand seewhat dwellswithin WHY? 1 S T Q U A R T E R This is Ludrein Salvador. I am your fellow STEMinist and learner too. Courses like General Physics have their edge in terms of having enormous formulas, equations, conversions, and it is not that quick to remember it all, right?
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CONTENTS VECTORS AND ADDITION OF VECTORS KINEMATICS: MOTION ALONG A STRAIGHT LINE AVERAGE AND INSTANTANEOUS ACCELERATION CIRCULAR AND PROJECTILE MOTION NEWTON'S LAWS OF MOTION CENTER OF MASS, IMPULSE, AND MOMENTUM ROTATIONAL MOTION GRAVITY PERIODIC MOTION 03 UNITS, PHYSICAL QUANTITIES, AND MEASUREMENTS 4 5 6 7 7 8 9 10 11 12
UNITS,PHYSICALQUANTITIES, ANDMEASUREMENTS
Memorize the unit conversions so you can solve the equations easily The more you understand the conversion, the easier it will be to solve the problem.
FUNDAMENTALQUANTITIES SIUNIT SYMBOL Length Mass Time Electric Current Temperature Amount of substance Luminous Intensity meter kilogram second Ampere Kelvin mol candela m kg s A K mol cd 80 m x 1 km 1000 m = 0.080 km
PHYSICAL QUANTITIES AND MEASUREMENT CONVERSION OF UNITS! METERS TO KILOMETERS 1 METER 1 METER 1 METER 1 METER 1 INCH 1 FOOT 1 CENTIMETER = = = = = = = 3.28 FEET 39.37 INCHES 100 CENTIMETERS 1000 MILLIMETERS 2.54 CENTIMETERS 12 INCHES 10 MILLIMETERS
Low accuracy Low precision High accuracy Low precision Low accuracy High precision High accuracy High precision recision refers to the closeness of two or more measurements to each other A P
TIPSN 'TOOLS!
04 ccuracy refers to the closeness of a measured value to a standard or known value.
To add vectors numerically, apply the Pythagorean theorem, as shown in the formula
R = x 2 y 2 + SECONDVECTOR FIRSTVECTOR x y TAIL ANALYTHICAL METHOD Complete the parallelogram. The diagonal of the parallelogram is the resultant vector u + v Place both vectors, u and v at the same initial point 01 02 03 + v u v u A A = y Ax tan-1 Ay Ax Ay 2 2+ Ax A = a b c a=side adjacent to angle b=side opposite to angle c=hypotenuse of triangle sin b c = cos a c = tan b a = Y X Z k j i O 05 The following formula can be used to solve a unit vector u -8i - 4j + 4k = (-8) + (-4) + (4) 2 2 2 -8i - 4j + 4k 6 4 2 1 1 = = < -6 6 6 , , u u > ADDITION OF VECTORS
vectorsand additionofvectors
AND VECTOR QUANTITIES
S V HEAD-TO-TAIL METHOD RESULTANTVECTOR
PARALLELOGRAM METHOD
2a 2b c2 + =
CAH TOA is a mnemonic for
the
trigonometric functions: sine, cosine, and tangent TIPS N' TOOLS! The representation of a unit vector
x, y, and z
I j, and k
Find the unit vectors for the vector whose head is located at coordinate A = <-8i – 4j –4k> SCALARQUANTITIES VECTORQUANTITIES Time•Mass•Distance•Length•Volume•Temperature•Energy•Speed•Power•Work Weight•Displacement•Acceleration•Force•Velocity•Impulse•Momentum
UNIT VECTORS
SCALAR
calars are quantities that may be completely defined by a single magnitude (or numerical value) ectors are quantities that have a magnitude as well as a direction
If two vector values are represented by two neighboring sides of a parallelogram, the diagonal of the parallelogram is equal to the product of these two vectors
below
SOH
remembering
meaning of three popular
inside the
axes in the directions designated by
is shown in the figure
SPEED & VELOCITY
peed is a scalar quantity with only a single magnitude Velocity, on the other hand, is a vector quantity, which means that it has both magnitude and direction.
AVERAGE VELOCITY
A
verage velocity is defined as a vector quantity. The change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs yields the average velocity.
INSTANTANEOUS VELOCITY
The instantaneous velocity, sometimes known as just velocity, is the number that informs us how fast an item is going somewhere along its route.
An object's instantaneous velocity is the limit of its average velocity as the elapsed time approaches zero, orthederivativeofxwithrespecttot.
01 02 03 04 05
Galileo was the first scientist to measure speed as a function of distance over time
A good illustration of immediate speed is a speedometer
Light travels at a speed of 186,282 miles per second, which may alternatively be written as 186,282 miles per second
In dry air, the speed of sound is 343.2 meters per second.
d s t d v t 06 Averagevelocity = Displacement between two points Elapsed time between two points �� = 2 1 2 1
WHERE:
��(��)=������ Δ��→0 ��(�� + Δ��) − ��(��) Δ�� ����(��) ���� = Δx =x - x f 0 kinematics:
DISPLACEMENT Δx = is displacement, x = is the final position, and; x = is the initial position. f 0
motionalongastraightline
speed = distance time time = distance speed distance = speed x time velocity = distance time time = distance velocity distance = velocity x time
S
The Earth's escape velocity is the speed required to escape the gravitational attraction of the planet It is traveling at a speed of 25,000 miles per hour ��= Δ�� Δ�� = �� �� �� ���� = �� ���� ��(��) �������� TANGENTIAL VELOCITY �� = 2��r �� PhysicsforKids SpeedandVelocity (2021) Ducksterscom https//wwwducksterscom/science/physics/speed and velocityphp#: text Interesting %20Facts%20about%20Speed%20and%20Velocity&text A%20speedometer%20is%20a%2 0great,escape%20from%20Earth’s%20gravitational%20pull
he velocity at the start of this interval is known as the initial velocity, and it is represented by the symbol v , whereas the velocity at the end is known as the final velocity, and it is represented by the sign v .
INSTANTANEOUS ACCELERATION
he limit of average acceleration is then instantaneous acceleration The time interval approaches 0, or acceleration is the derivative of velocity.
It is also important to think about ac in terms of angular velocity. By substituting v = rω into the above formula, we obtain:
If T is the period of motion, or the time it takes to complete one rotation (2π rad), then the angle that the position vector possesses at any given momentisωt.
PROJECTILE MOTION:
VERTICAL DIRECTION
If the particle's speed changes, it experiences tangential acceleration, which is the time rate of change of the magnitude of the velocity:
he following equation can be used to calculate the horizontal direction When the velocity in a given direction is constant, we may use ∆�� = ���� to calculate how far the item goes in that area
Because the vertical acceleration is constant, we may use one of the four kinematic formulae provided below to solve for a vertical variable.
∆�� ∆�� �� − �� �� − �� 0 0 �� = =
T 0 f ��(��) = �� ���� ��(��) 07 2 ∆��=( ��+��0 )�� ∆��=�� �� + 0 1 2 ������ 2 averageand instantaneousaccelEration
AVERAGE ACCELERATION
T circularand
projectilemotion
HORIZONTAL DIRECTION ∆�� = ������
T
0 �� = �� + �� �� �� = �� 2 �� �� 2 0 + 2�� ∆�� 01 02 03 04 CENTRIPETALACCELERATION ���� = ��2 r CENTRIPETAL FORCE ���� = m ��2 r ����= (rω) �� r = 2 r 2 ω r = 2
��= 2π T NON-UNIFORM CIRCULAR MOTION
��
���� ���� �� �� �� �� �� �� �� �� �� ��
=
01 LAW OF INERTIA
ewton's first law states that if an object's net force is zero, the object will have zero acceleration. This does not necessarily imply that the item is at rest, but it does imply that its velocity is constant.
The mass of an object is used to calculate its inertia. The mass of an item may be calculated by measuring how difficult it is to accelerate it. The greater an object's mass, the more difficult it is to accelerate.
LAW OF ACCELERATION
ewton's second law specifies how quickly an item will move for a given net force
How may we apply Newton's second law?
02 03
WHERE:
a = is the acceleration of the object.
ΣF = is the net force on the object.
m = is the mass of the object.
HORIZONTAL DIRECTION VERTICAL DIRECTION
LAW OF INTERACTION ffun un ffacts! acts!
https://mammothmemorynet/images/user/base/Physics/Newtons%20laws%20of%20motion/example-4-balloon-action-reaction66918c0jpg
According to the first law of motion, an object at rest will remain at rest.
The second law of motion asserts that acceleration happens when a force acts on mass, and;
The third law of motion states that there is an equal and opposite response to every action.
��
Σ
=
F m
�� = ΣFₓ m �� = ΣFᵧ m
08
newton'slawsof motion
N N
CENTER OF MASS
GEOMETRIC CENTER
A planar figure's centroid, also known as its geometric center, is the arithmetic mean position of all its points
Note: The Center of mass is the same as the centroid when the density is the same throughout
enter of mass is a point representing the mean position of the matter in a body or a system
HOW DO WE DETERMINE THE POSITION OF THE CENTER OF MASS?
omentum is a measure of mass in motion: how much mass is involved in how much motion. It is commonly denoted by the sign p.
WHERE:
p = given symbol of momentum m = is the mass v = is the velocity
A constant net external force applied to a system for a certain time interval causes a change in momentum equal to the product of the force and the time interval, Ft = p
whatis
exceptional aboutthecenter ofmass?
The center of mass of an object or system is noteworthy because it is the place at which any uniform force acting on the object acts. This is helpful because it makes it easier to tackle mechanical issues involving the motion of irregularly shaped objects and complex systems
COLLISIONS
NOTE: Momentum has a standard unit of measurement of kg m/s and is always expressed as a vector quantity.
As a result, every change in momentum caused by an acceleration may be represented as:
Impulse refers to the total impact of a force acting over time It is commonly denoted by the sign J and is measured in Newton-seconds
We have the following constant forces:
Elastic Collisions = Momentum and kinetic energy are both preserved. Inelastic Collisions = Momentum is preserved
If two particles collide elastically, the velocity of the first particle following the collision may be stated as:
If two particles collide elastically, the velocity of the second particle after the impact may be stated as:
09 ��₁ m₁x₁ + m₂x₂ m₁m₂ ��₂ Center of mass For two masses: xcm = m₁ xcm m₂ ��₁∙ ��₁ + ��₂ ∙ ��₂ ��₁ + ��₂ �� = ���� ��₁ ∙ ��₁ + ��₂ ∙ ��₂ ��₁ + ��₂ �� = ����
(m +m ) (m m ) 2 1 2 1 v =2f 2⋅ m1 (m +m ) 2 1 v + 1i v2i v = (m +m ) v + (m m ) 2⋅m 1 2 2 1 2 (m +m ) 2 1 v 1i 2i 1f centerofmass, impulse&momentum
C FOR X-DIRECTION: FOR Y-DIRECTION: MOMENTUM AND IMPULSE �� = �� ∙ ��
M
∆��=��∙∆�� ∆��=��∙��∙∆�� ∆��=��∙∆�� �� = �� ∙ ∆��
OF CONSERVATION OF MOMENTUM CONSERVATION OF MOMENTUM TOTAL INITIAL MOMENTUM = TOTAL FINAL MOMENTUM �� �� + �� �� = �� �� + �� �� �� �� �� �� �� �� �� ��
LAW
�� �� �� �� Collisons|BoundlessPhyscs(2013)Lumenlearningcom https//courseslumenlearningcom/boundess-physics/chapter/colisons/
rotationalmotion
ROTATIONAL QUANTITIES:
ANGULAR DISPLACEMENT
T
heconnection describesangular velocity,whichisthe rateofchangeof angulardisplacement.
Rotational acceleration is another name for angular acceleration. The size or length of the acceleration vector is directly proportional to the rate of change in angular velocity.
Angular displacement is a vector quantity, which implies it has a size and a direction
Angular displacement is defined as follows:
S = An angular displacement occurs when a body rotates about a rotation axis, altering its angular position from θ1 to θ2
WHERE:
∆
= ��2 − ��1
NOTE: 1 rev = 2π rad
ANGULAR VELOCITY
�� = ��r
��=2π�� Axis of rotation
ANGULAR ACCELERATIONWHERE:
Δω = is the angular velocity change Δt = is the time change (rad/s)/s or rad/s are the units of angular acceleration
2
f = frequency in revolution/s
I = L ��
WHERE:
Momentum
WHERE:
TOOLS!
MOMENT OF INERTIA 10
The Newton-meter is the SI unit for torque. Torque can be either static or dynamic in nature
The moment of inertia I of an item is the total of mr for all of its point masses. That is,
ALWAYSREMEMBER! �� = ∑���� 2
A static torque is one that produces no rotational acceleration
The dynamic torque is the quantity connected to the power on a spinning machine.
TORQUE IS DEFINED AS FOLLOWS:
�� = �� ∙ �� �� = �� ∙ �� sin ��
r S =
r
r S = ��= �� r
= �� r
∆�� ∆��
��
�� = average
∆�� ∆��
α =
r S
Because S = 2��r for a complete circle, 2 radians = 360 degrees and one radian = 180/�� degrees = 573 degrees ��
∆θ is positive for counterclockwise rotation and negative for clockwise rotation.
The unit of angular velocity is rad/s. OR
NOTE: If ω increases, then α is a positive value If ω declines, then α is a negative value
= mr2 I =
m =
r
ROTATIONAL INERTIA I = inertia L = Angular
�� = angular velocity I
inertia
Mass
= Radius
TORQUE
Torque is a force that may cause an item to revolve around an axis.
ravity is the invisible force that pulls everything to the ground (the surface of the Earth) Gravity affects everything on Earth, including people, plants, animals, and objects.
NEWTON’S UNIVERSAL LAW OF GRAVITATION
Newton's law of gravitation has the following equation:
Gm₁m₂ r² F��=
How to find the gravitational field strength
Itisdefinedas:
Gm₁m₂ r²m₂ �� =
G = is the gravitational constant which is equal to �� = 6.67 ��10 ���� /���� �� and �� = are the masses
F�� m₂ �� = 01 02 03
�� = Gm₁ r²
The gravitational field is the region of space around a body where another body experiences gravitational attraction
WHERE: Mass
ORBITAL VELOCITY
GRAVITATIONAL POTENTIAL ENERGY
GRAVITATIONAL
FIELD
Gravitational potential energy is the energy that an object has due to its position in a gravitational field The symbol Ug is commonly used to represent gravitational potential energy
= ���� ∙ ℎ
If the object is lifted straight up at a constant speed, the force required to lift it is equal to its weight in milligrams (mg)
KEPLER’S LAWS OF PLANETARY MOTION
o calculate the orbit velocity for a circular orbit, multiply the gravitational force by the needed centripetal force
2 2 -11 1 2 = ��ᶜ GM r
WHERE:
v = the orbital velocity of an object (m/s)
G = the universal gravitational constant, G = 6.67x10 N∙m /kg
-11 2 2 24
m = the mass of the Earth (5.98 x 10 kg)
r = the distance from the object to the center of the Earth
01 02 03
The Law of Orbits states that all planets orbit the Sun in elliptical orbits. One of the foci is the Sun.
The Law of Areas states that a line linking two planets sweeps out the same amount of space in the same amount of time.
The Law of Period states that the square of a planet's period is proportional to the cube of its semi-major axis. The connection, commonly known as Kepler's third rule, asserts that a planet's orbital period squared is proportionate to its semimajor axis cubed, or
ᵀ
² = 4π² GM a³
canbeexpressed assimply T²=a³ OR
WHERE:
When measured in the following units:
T = Earth years
a = Astronomical units AU (a = 1 AU for Earth)
M = Solar masses M
Then 4π²
G =1
P = denotes the orbital period, or the time required to complete one round around the Sun. a = semi-major axis
11
gravity
G
����
���� = ����ℎ
T
�� = �� 2 3
periodicmotion
eriodic motion is a repetitive motion of an object in which the item returns to a set place after a predetermined time period
PROPERTIES OF PERIODIC MOTION
TIMEPERIOD(T): 01
The period (T) of a body in periodic motion is the amount of time necessary to complete a full to-andfro motion
FREQUENCY(F):02
It is the number of times a motion is repeated in one second The frequency unit is Hz (Hertz). Frequency is connected to time in the following way:
AMPLITUDE(A): 03
The greatest displacement of a body from its equilibrium position is defined as its amplitude of vibration
Angular frequency (ω) is sometimes used instead of frequency The most common unit of measurement for angular frequency is radians per second. The following is the connection between angular frequency and frequency:
��= 1 T �� = 2���� or 2�� T
SIMPLE HARMONIC MOTION
SMH, or Simple Harmonic Motion, is an oscillatory motion in which the net force on the system is a restorative force.
HOOKE’S LAW
Hooke's law is the term given to this connection between force and displacement: �� = −����
WHERE:
F = restoring force
x = the displacement from equilibrium or deformation
k = is a constant associated with the difficulty of deforming the system (often called the spring constant or force constant).
APPLICATIONS FOR HOOKE’S LAW (Simple Harmonic Motion)
SPRING 01 �� = −���� spring
CalculatingPeriodandFrequency oftheSpring-MassSystem
The period of a spring-mass system is proportional to the mass squared and inversely proportional to the spring constant squared.
Angular Frequency of a Spring: k m �� = �� =2
SIMPLE PENDULUM 02
Period taken by the simple pendulum:
T = is period.
P
�� = 2�� L g
L = is pendulum length.
g = is the acceleration due to gravity.
PHYSICAL PENDULUM 03
Period taken by the physical pendulum is:
WHERE:
WHERE: �� = 2�� I mgL ��
I = is the moment of inertia.
S
g = is the acceleration due to gravity
L = is length of the object.
12
k
�� m
��
P
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