Module 1 - Measurement
Fundamental/Base Quantities - group of physical quantities that can be measured without relying on other quantities; (mass, length, molar mass, luminous intensity)
Derived Quantitites - use any combination of fundamental quantities; (velocity, acceleration, rate, force)
Convertion of Units - convertion between different units for the same quantity
Unit prefixes - placed before the symbol of a unit to specify the order of magnitude of the quantity; used for very large or very small numbers |
Notations
Regular Notation |
standard way of writing numbers |
seven hundred sixty = 760 |
Scientific Notation |
convenient and shorthand way of writing really large or really small numbers |
280,000,000 = 2.8 × 108 |
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0.000817 = 8.17 × 10-4 |
Module 2 - Accuracy and Precision
Significant Figures - digits that carry meaningful contributions to its measurement resolutions
1. Non-zero digits are always significant
2. Any zeroes between two significant digits are significant
3. A final zero or trailing zeroes in the decimal portion only are significant
13000 = 2 sig. figs.
0.00410 = 5 sig. figs.
9.6010 × 108 = 5 sig. figs.
Accuracy - describes how close a measured value is to the true value, it is expressed using relative error:
Relative error = |(measured value - expected value)/(expected value)| × 100
Precision - degree of exactness with which a measurement is made and stated; for example, 1.324 is more precise than 1.3; it is expressed as a relative or fractional uncertainty
Relative Uncertainty = (uncertainty / measured quantity) × 100 |
Module 3 - Vector and Scalar Quantities
-Scalar quantities are described by a magnitude (size or numerical value) only; (Mass - amount of matter in your body = g or kg)
-Vector quantities give both the magnitude and direction; (Weight - amount of gravitational force exerted on the matter = kg⋅m/s2 or N)
Vectors and Addition of Vectors
Vectors - can be represented by a ray line →; the length of the arrow represents the magnitude while the direction of the arrow represents the direction of the vector; the tail is called the initial point or the origin
Vector Direction - North, South, East, West; however, some vectors are projected to a certain degree: 30° North
Magnitude of a Vector - shown by the length of the arrow with a chosen scale
Resultant Vector - vector sum or difference of all individual vectors |
Methods of Adding Vectors
Graphical |
Analytical |
choose appropriate scale and frame of reference |
Vectors in the same or opposite direction must be added with sign convention; North and East (↑→) are positive and South and West (←↓) are negative |
use tools of measurement (basta may minemeasure ka bes) |
Vectors perpendicular or in right-angle, use pythgorean theorem for magnitude and trigonometric functions for direction |
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Vectors not perpendicular, use law of cosine for magnitude and law of sine for direction |
-Another way is the component method were the x and y components of the vectors are determined to find the resultant
Module 4 - Displacement and Velocity
Motion - can also be described through visual representations like graphs
Acceleration - rate of change in velocity
Constant Accelaration - when an object is moving with the same rate of change of velocity
Displacement - shortest distance from an object to the reference point; areas of velocity vs. time curve
Velocity - rate of change of position; areas of displacement vs. time curve
Average Velocity - total displacement of a body over a time interval
Instantaneous Velocity - velocity at a specific instant in time |
Module 5 - Acceleration
Acceleration - slope in velocity vs. time; if velocity is constant then there is no acceleration
Instantaneous Acceleration - acceleration at any instant time (only one point in time) (△v)/(△t)
Average Acceleration - (total velocity)/(total elapsed time) |
Slope of acceleration
-Velocity (Y) is divided by Time (X) in a velocity-time graph and position-time graph
-To get the total acceleration (only in velocity-time graph), get the summation of all calculated acceleration and divide it by the points in the graph (time periods); the unit will be m/s2
Module 6 - Uniformly Acc. Motion & Free-Fall
Uniformly Accelerated Motion (UAM) - motion with constant acceleration; velocity changes by equal amounts in equal intervals
Free-Fall/Vertical Motion - a uniformly accelerated motion; objects in motion under gravity only (g = 9.8 m/s2) |
UAM equations in one dimension
UAM equations in one dimension (free-fall)
-the a is replaced by g, -9.8 m/s2 for downward acceleration and vice versa
Module 7 - Components of Projectile
Projectile - any object that is thrown or otherwise projected into the air
Trajectory - characteristic path of a projectile; a parabola
Projectile Motion - describes the movement of a projectile along its trajectory |
Module 8 - Time at Max Height of Trajectory
Half Time of Flight - time it takes for a projectile to reach the maximum height; t = √(2dᵧ/g)
(where dᵧ = (Vᵢᵧt)/(½gt²), t = time of flight, g = acceleration due to gravity)
Total time of flight - double the half time of flight; t = (Vᶠᵧ - Vᵢᵧ)/g
(where Vᶠᵧ = final vertical velocity, Vᵢᵧ = initial vertical velocity, g = acceleration due to gravity, t = time of travel)
Maximum Height - highest point the projectile can reach in the trajectory; the displacement formula is used: dᵧ = (Vᵢᵧt)/(½gt²)
(where dᵧ = vertical displacement, Vᵢᵧ = initial vertical velocity, t = time of flight, g = acceleration due to gravity)
Range of the Projectile - distance from the initial point on the ground to the final point it reaches; dₓ = Vᵢₓt
(where dₓ = range, Vᵢₓ = initial horizontal velocity, t = time of flight)
X and Y Component of the Velocity - used to determine the graph of trajectory; Vᵢₓ = Vᵢ cos θ and Vᵢᵧ = Vᵢ sin θ
(where Vᵢₓ = initial horizontal velocity, Vᵢᵧ = initial vertical velocity, Vᵢ = inital velocity, θ = angle of trajectory) |
Module 9 - Circular Motion
Circular Motion - motion along a circular path in which the direction of the velocity is always changing; the speed is tangent to the path and the force towards the center is constant
Tangential Speed (vᵣ) - speed of an object in circular motion; depends on the distance from the object to the center. If the tangential speed is constant, the motion is said to be uniform circular motion
Centripetal Acceleration - acceleration directed toward the center of the circular path; centripetal acceleration = (tangential speed)²/(radius of circular path) or a꜀ = vₜ²/r
Tangential Acceleration (aᵣ) - acceleration of a certain object in a circular motion due to change in speed
Non-uniform Circular Motion - an object moving in a circular path with changing velocity
Centripetal Force - "center-seeking force," net force directed toward the center of the circle; Fₙₑₜ = F꜀ₑₙₜᵣᵢₚₑₜₐₗ
(where Fₙₑₜ = m×a; Fₙₑₜ = F꜀ₑₙₜᵣᵢₚₑₜₐₗ = mass × centripetal acceleration)
F꜀ₑₙₜᵣᵢₚₑₜₐₗ = mass × (tangential speed² / radius of circular) OR F꜀ = mvₜ²/r |
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Module 10 - First Law Motion: Law of Inertia
Contact Forces - two objects having physical contact with each other (pushing or pulling)
+ Tension Force (t) - force transmitted through a string, rope, cable, or wire, when it is pulled tight by forces avting on its opposite ends
+ Air Resistance - special type of frictional force that acts upon objects as they travel through the air
Normal Force (N) - support force exerted upon an object that is in contact upon another stable object
+ Friction (Ff) - force exerted by a surface as an object moves across it or makes an effort to move it across
+ Applied Force (Fa) - force applied to an object by a person or another object
Non-Contact Forces - objects are subjected to a force but do not need to be in contact with each other
+ Gravitional Force - "Weight (W)"; the force with which the earth, moon, or other massively large object attracts another towards itself
Newton's First Law of Motion: Law of Inertia
-an object at rest stays at rest and an object in motion stays in motion with the same velocity unless acted upon by an unbalanced force
-valid for an inertial reference frame
Inertia - tendency of an object to resist changes in its motion; the heavier the mass, the greater is the inertia
Inertial Frame of Reference - frame of reference with constant velocity and non-accelerating;
For example, you are standing, and your speed relative to the ground is zero, but your speed relative to the sun is 2.97x104 m/s
Free Body Diagram - shows relative magnitude and direction of all forces acting upon an object; direction of arrow shows direction of force and the size of arrow shows the magnitude of force |
Module 11 - 2nd Law of Motion: Law of Acceleration
-The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object
-a is directly proportional to F where m is constant
-a is inversely proportional to 1/m where F is constant
acceleration = (net force)/(mass); a = F/m; F = ma
Weight - gravitational force exerted by a large body, measured in Newton (N); W = mg |
Module 12 - 3rd Law of Motion: Law of Interaction
-when one object exerts a force (action) on a second object, the second object exerts a force (reaction) on the first object that is equal in magnitude but opposite in direction
F₁ = F₂ or force of action = force of reaction
Friction - force that opposes the motion between two surfaces that are in contact
Coefficient of Friction - level of friction that different material exhibit; μ = Ff/N
(where μ = coefficient of friction, Ff = friction, N = normal force)
Static Friction (fₛ) - acts on objects when they are resting on a surface
Sliding Friction or Kinetic Friction (fₖ) - force that acts between moving surfaces |
Module 13 - Work
Work - amount of force applied on an object over a displacement;
W = F×d
SI unit of Joules (J)
If the force is at an angle to the displacement using dot product:
W = F x d x cos θ |
Module 14 - Power
Power - measures rate at which work is done or energy is transformed; P = (Work)/(Time)
SI Unit: Joule per second (J/s)
if Force and Displacement were given: P = (Force)(Displacement)/(Time)
if it's in an angle: P = (Force)(Displacement)(cosine Ø)/(Time)
if Velocity is given: P = (Force)(Velocity)
if it's in an angle: P = (Force)(Velocity)(cosine Ø) |
Module 15 - Energy and Energy Conservation
Energy - property of an object or system that enables it to do work; measured in Joules
Mechanical Energy - energy due to the position of something or the movement of something; sum of kinetic and potential energy and therefore always stay the same
+ Potential Energy - stored energy; form of energy due to the position of an object to the other objects or a reference point.
Gravitational Potential Energy - energy due to the object’s position relative to the gravitational source; depends on the height from a zero level
GPE = (mass)(acceleration due to gravity)(height) or GPE = mgh
Elastic Potential Energy - energy stored in a compressed or stretched spring or object
EPE = (½) (spring constant)(distance compressed or stretched)² or EPE = ½kx²
+ Kinetic Energy - Work done to change the speed of an object; depends on mass and speed
KE = (½)(mass)(speed)² or KE = ½mv²
Work-Energy Theorem - whenever work is done, energy changes; if work is done on an object, the net work is equal to its change in kinetic energy
Workₙₑₜ = change in kinetic energy or Workₙₑₜ = △KE or
Workₙₑₜ = ½mv²(final) - ½mv²(initial) |
Module 16 - Center of Mass
-The formula for computing the velocity of the center of mass of a system in three dimensions may be obtained by replacing x, y, and z by vx, vy and vz, respectively.
Module 17 - Momentum and Impulse
Momentum - describes the difficulty in changing the state of motion of a moving object; p = mass×velocity
Impulse (I) - product of the force and the time it takes for the force to be applied; SI unit of kg.m/s
I = Force×time or I = m(vf - vi)
Impulse-Momentum Theorem - since p = mv, I = △p |
Module 18 - Conservation of Momentum
Law of Conservation of Momentum - the total momentum before the collision is equal to the momentum of the system after the collision; pf = pi
Coefficient of Restitution (e) - negative ratio of the relative velocity of two colliding bodies after a collision to the relative velocity before the collision; e = (vₓ₂ - vᵧ₂)/(vₓ₁ - vᵧ₁)
(where vₓ₂ and vᵧ₂ =velocities of bodies X and Y after collision, vₓ₁ and vᵧ₁ = velocities of bodies X and Y before collision)
The coefficient of restitution can have a value from 0 to 1, depending on the type of collision
Elastic Collision - both momentum and kinetic energy are conserved; the coefficient of restitution is equal to 1
Inelastic Collision - total momentum is conserved but the total kinetic energy is not conserved, some of the kinetic energy goes into other forms like heat, sound, and permanent deformation; the coefficient of restitution for inelastic collision is between 0 to1
Perfectly Inelastic Collision - interacting bodies stick together and move as one after a collision; the coefficient of restitution for inelastic is 0 |
YEY! you finished q1, I am so proud of you :)
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