1. Unit 1: Kinematics
1.1. 1.1 Motion in one dimension
1.1.1. Vectors and quantities
1.1.1.1. Position
1.1.1.1.1. (is a vector integrated from velocity)
1.1.1.2. Distance
1.1.1.2.1. (scaler)
1.1.1.3. Displacement
1.1.1.3.1. (is a vector)
1.1.1.4. Velocity (v)
1.1.1.4.1. (is a vector derrived from position)
1.1.1.4.2. speed but with direction kept in mind/ speed + direction
1.1.1.4.3. Velocity is ALWAYS tangent to the path (whether circular motion path or projectile motion path)
1.1.1.4.4. Solving for v
1.1.1.5. Speed
1.1.1.5.1. is a scaler quantity
1.1.1.5.2. is the magnitude of velocity ONLY applies to constant v
1.1.1.5.3. is velocity if it had no sign (ONLY applies to constant v)
1.1.1.6. Acceleration (a)
1.1.1.6.1. (is a vector derrived from velocity)
1.1.1.6.2. Solving for a
1.1.1.6.3. constant velocity in circle has acceleration because direction is constantly changes
1.1.2. Freefall
1.1.2.1. Vertical motion, with the only force acting on the object is gravity
1.1.2.2. Acceleration in Freefall
1.1.2.2.1. Positive y axis: a=-gravity (so a is constant-> K.E)
1.1.2.2.2. Negative y axis: a=gravity (so a is constant-> K.E)
1.1.2.3. Velocity in Freefall always decreasing from positive initial to final, with mid point in time being 0 in velocity
1.2. 1.2 Motion in two dimensions
1.2.1. Projectile Motion
1.2.1.1. How to identify: ✅ Object is launched horizontally and vertically. ✅ Gravity is the only force acting. ✅ No additional propulsion during flight. ✅ Vx=Constant ✅ Motion in y is in freefall
1.2.1.1.1. Equations used in P.M
1.2.1.2. Definition: A projectile is any object given an initial velocity that then follows a path determined by the effects of gravity
1.2.1.3. Unique Elements in P.M
1.2.1.3.1. Range: The total value of x, starts at x0 and ends at xf
1.2.1.3.2. Max Height: Since it is freefall, maximum height is at half range
1.2.1.4. Solving Cases
1.2.1.4.1. When Two different times with same displacement/position are the missing variable: use quadratic equation k.e because it gives two values for time
1.2.2. Solving 2D Problems
1.2.2.1. How to solve: Same as solving 1D problems, but calculating for x and y components separatly, then finding vector and its magnitude, using pythagorean theorum and inverse of tan function
1.2.2.1.1. Other cases may require derriving/integrating values. When asking for x and y, remember to look for the x and y components of position seperately
1.2.2.2. Method of solving: (The basic idea minus the specific equations can be applied to 1d Motion as well)
1.2.2.2.1. 1. State the given and state what the question requires.
1.2.2.2.2. 2. Jot down all equations we have (If calculus is needed, find new functions and the rest is figureoutable)
1.2.2.2.3. 3. Tick everything we have off those equations
1.2.2.2.4. 4. Use equations where only one missing variable (that is relevant) is present, if not available, find other missing values of the equation using other equations to be able to solve
1.2.2.2.5. 5. Replace known values and solve
1.2.2.3. Concepts to Keep in Mind obout 2D Motion
1.2.2.3.1. V avg = ∆x ∆y ---- i + ---- j ∆t ∆t
1.2.3. Relative Motion
1.2.3.1. Vab=Vac+Vcb
2. Unit 2: Newton's Laws of Motion
2.1. Forces
2.1.1. Units
2.1.1.1. Newtons
2.1.1.2. f=ma
2.1.1.3. f=kg*m/s^2
2.1.1.4. dimensional formula: f=MLT^2
2.1.1.5. Net Force=mass*acceleration
2.1.1.6. All external Forces acting on a system=mass of the system*acceleration of system
2.1.2. What can they do:
2.1.2.1. Summary: External Forces can cause change in: - The magnitude of velocity - The direction of velocity In other words forces change or cause acceleration
2.1.2.1.1. Note: Forces internal to a system cannot affect the motion only unbalanced external forces determine the acceleration of the system
2.1.2.2. Effect of Forces on Velocity
2.1.2.2.1. Forces acting parallel to v can change the magnitude of vector v
2.1.2.2.2. Forces acting perpendicular to v can change the direction of vector v
2.1.2.3. Effect of Forces on Acceleration
2.1.2.3.1. F=ma shows that Forces cause acceleration or can at least change it
2.1.3. Can be categorized by:
2.1.3.1. Contact or no contact
2.1.3.2. Internal within the object (not considered net force) or external acts on the object (considered as a part of net force)
2.1.3.3. Push or pull
2.1.4. Distance Forces
2.1.4.1. Fg /W
2.1.4.1.1. Force of Gravity or Weight
2.1.5. Contact Forces
2.1.5.1. T
2.1.5.1.1. Tension
2.1.5.2. F꜀
2.1.5.2.1. Centripetal Force
2.1.5.3. Fs
2.1.5.3.1. Spring Force
2.1.5.4. Fₐ
2.1.5.4.1. Applied Force
2.1.5.5. Fdrag
2.1.5.5.1. Drag Force or Air resistance
2.1.5.6. Normal Force
2.1.5.6.1. Normal force is the reaction of a surface in contact to a system
2.1.5.6.2. It's direction is always perpendicular to the surface
2.1.5.7. Friction
2.1.5.7.1. Characteristics
2.1.5.7.2. Coefficient of Friction
2.1.5.7.3. Types:
2.2. Newton's 3 Laws
2.2.1. First Law
2.2.1.1. Law of inertia (Inertia is the tedency of an object to resist acceleration)
2.2.1.1.1. An object at rest remains at rest at equilibrium (when net force=0)
2.2.1.1.2. An object at motion remains in motion at equilibrium (when net force=0)
2.2.2. Second Law
2.2.2.1. F=ma
2.2.2.1.1. The sum of all external forces is equal to the mass of the system* its acceleration
2.2.3. Third Law
2.2.3.1. Every Action has an equal and opposite reaction
2.2.3.1.1. Object A exerts a force on object B, object B exerts a force on object A that... - equal in magnitude - the same type of force - is a push/pull if force of A was a push/pull - Forces occur simultaneously - is in the opposite direction
2.3. Cases
2.3.1. Translational Equilibrium
2.3.1.1. No net force, but object moves at constant velocity in one direction
2.3.2. Ideal Situation
2.3.2.1. Mass and fricition of rope/cord is negligable
2.3.2.2. friction is negligable
2.3.3. Equilibrium
2.3.3.1. No Net force
3. Unit 3: Work, Energy, and Power
3.1. Work
3.1.1. Work
3.1.1.1. Work is the energy transferred to or from an object via the application of force along a displacement
3.1.1.2. Work is done by forces on a system More specifically, the components parallel to the displacement In other words, forces transfer energy to and from an object Work is analyzed based on individual forces, net work is sum of indivdual works
3.1.1.3. Unit of work is Joules since it describes energy
3.1.1.4. The scaler/dot product of a force and the displacement of the object W= Fdcosθ
3.1.1.5. Work is a signed scaler but the sign does not describe a direction as in the case of a vector, it describes energy flow • Positive: Energy in, energy done on the system • Negative: Energy out, energy done by the system The sign is dependent on the cosine of the angle between the force and the displacement
3.1.2. Net Work Energy-Theorem
3.1.2.1. Net Work:
3.1.2.1.1. Sum of all individual works on an object
3.1.2.1.2. Wnet= Fnetdcosθ
3.1.2.2. Net work Theorem:
3.1.2.2.1. states that Wnet= Chnage in kinetic energy Wnet= ΔKE Wnet= KEf-KEo Wnet= (1/2 m vf²)-(1/2 m vo²)
3.2. Mechanical Energy
3.2.1. 2 types:
3.2.1.1. Kinetic Energy (energy gained due to motion)
3.2.1.1.1. KE= 1/2mv²
3.2.1.2. Potential Energy (energy gained to perform an action)
3.2.1.2.1. Elastic Potential Energy
3.2.1.2.2. Gravitational Potential Energy
3.2.2. Law of conservation of mechanical energy (and other equations)
3.2.2.1. Ko+Uo=Kf+Uf
3.2.2.1.1. Always true, however final can be smaller than initial, because sometimes we lose energy in the form of heat, etc, because of decipative forces like friction, air resistance, drag force
3.2.2.2. ΔKE=-(ΔU)
3.2.2.3. ME=K+U
3.2.2.3.1. Law of conservation of total mechanical energy
3.2.2.4. If, Ko+Uo not= Kf+Uf Then, Ko+Uo not= Kf+Uf+ Work of Decipative Force
3.2.2.5. ΔME= Work of Decipative Force
3.2.2.6. -dU ---- = F dx
3.3. Power
3.3.1. rate at which energy is gained or released
3.3.2. Power: change in energy/t Power: dK.E/dt Power: W/t Power: F . v
3.3.3. units: Watt=1 Joule/second
3.4. Energy: ability to do work, which is the ability to exert a force causing displacement of an object What causes things to move
4. Unit 4: Systems of Particles and Linear Momentum
4.1. Key concepts
4.1.1. Linear Momentum (vector)
4.1.1.1. Unit:
4.1.1.1.1. kgm/s N*s
4.1.1.2. Meaning:
4.1.1.2.1. It is the product of velocity as a vector and mass
4.1.1.2.2. inertia in motion
4.1.1.3. Vector Features:
4.1.1.3.1. same direction as velocity, and velocity is the same direction as position, so also same direction as position or tangent to path
4.1.1.3.2. magnitude: m * |v|
4.1.1.4. Equations:
4.1.1.4.1. p=mv
4.1.1.4.2. ∫p=K.E
4.1.2. Impulse (vector)
4.1.2.1. Units:
4.1.2.1.1. kg*m/s Newton*second
4.1.2.2. Meaning:
4.1.2.2.1. Change in momentum
4.1.2.3. Vector features:
4.1.2.3.1. magnitude: found through equations, by spliting it up into components then pythagorean theoreming
4.1.2.3.2. direction: same as direction of Fnet or inverse tan if that is not available
4.1.2.4. Equations:
4.1.2.4.1. J = Fnet * Δt
4.1.2.4.2. J = Fnet dt
4.1.3. Collisions
4.1.3.1. Meaning:
4.1.3.1.1. A collision is when components of a system experience displacement and no net external forces outside the ones they exert on each other exist
4.1.3.2. Types:
4.1.3.2.1. Elastic Collision:
4.1.3.2.2. Inelastic collisions:
4.1.4. It's Rocket Science :slightly_frowning_face: :
4.1.4.1. Propulsion: The very unique situation where a rocket loses a part of its mass with time to propel itself forward. All equations are derrived from conservation of momentum of this situation
4.1.4.2. Propulsion Equations:
4.1.4.2.1. a = -Ve dm --- * ---- m dt
4.1.4.2.2. v = vo + ve ln (mo/m)
4.1.4.2.3. F = -Ve * dm ------------ dt
4.1.5. Center of Mass:
4.1.5.1. Meaning: Average position relative to mass
4.1.5.2. Key features:
4.1.5.2.1. If you have center of mass: you could derrive it in terms of dt and end up with velocity of the center of mass and go further to
4.1.5.2.2. COM is a position!! You could find it's x position and y position (so it is also a vector)
4.1.5.2.3. COM is the point that describes the motion of a whole system. If I have an unsymmetrical projectile
4.1.5.3. Methods of Finding:
4.1.5.3.1. Σ m1*x1+m2*x2...mnxn ------------------------------ m1+m2+....mn
4.1.5.3.2. Xcm= 1/m ∫r dm
4.2. Laws
4.2.1. Impulse-momentum theorem
4.2.1.1. Impulse is the change in momentum
4.2.1.2. I= Δp
4.2.2. Conservation of total momentum
4.2.2.1. in any collision (remember closed system no external net forces only internal), momentum initial is equal to momentum final
4.2.2.2. mv+mv=mv+mv
4.2.3. Force of Impact approximation
4.2.3.1. Fnet/time=impusle, Howeverr, for Fnet to cause an impulse usually an overpowering Force can be pinpointed as the approximate Fnet that causes the impulse and that is reffered to as Force of Impact
4.3. Solving startegies
4.3.1. Before/After collision
4.3.1.1. 1. Before Collision
4.3.1.1.1. ma voa
4.3.1.1.2. mb vob
4.3.1.2. 2. After collision
4.3.1.2.1. ma vfa
4.3.1.2.2. mb vfb
4.3.1.3. 3. Separate v into components!!! then solve using momentum in x direction and in y (basically rememebr that momentum and velocity are vectors)
5. Unit 5: Rotation
5.1. Rotational Counterparts
5.1.1. Rotational Kinematics
5.1.1.1. counterparts
5.1.1.1.1. angular displacement (θ)
5.1.1.1.2. angular velocity (ω)
5.1.1.1.3. angular acceleration (α)
5.1.1.1.4. kinematic equations
5.1.2. Rotational Dynamics
5.1.2.1. Torque (τ)
5.1.2.1.1. Equations
5.1.2.1.2. meaning
5.1.2.1.3. Unit
5.1.3. Energy in Rotation
5.1.3.1. Forget about potential
5.1.3.1.1. It remains mgh, since kinetic means motion, and rotational motion --> motion related energy
5.1.3.2. There are two kinds of kinetic energy
5.1.3.2.1. Linear
5.1.3.2.2. rotational
5.1.3.3. total mechanical energy becomes mgh + 1/2kx^2 + 1/2mv^2 + 1/2Iω
5.1.4. Angular Momentum, etc in rotation
5.1.4.1. angular momentum
5.1.4.1.1. L = Iω
5.1.4.1.2. Unit : kgm²/s
5.1.5. Inertia
5.1.5.1. Inertia: The ability of an object to resist acceleration
5.1.5.2. Linear inertia is described through Mass
5.1.5.2.1. more mass more linear inertia -> resistance to change that's about it
5.1.5.3. Rotational inertia is:
5.1.5.3.1. For a point-particle: I=mr^2
5.1.5.3.2. For a continuous body: ∫r^2 dm
5.1.5.3.3. For an object made of several masses with known I: sum of all I
5.1.5.3.4. For an object with known I when axis is at center: Parallel axis theorem
5.1.5.3.5. Maximizing Rotational Inertia or what makes rotational inertia large
5.2. Rotational Equilibrium
5.2.1. Conditions
5.2.1.1. Fnet=0
5.2.1.2. Net Torque=0
6. Unit 6: Oscillations
6.1. Simple Harmonic Motion (Periodic Motion)
6.1.1. meaning: A motion of back and forth around a certain position of equilibrium (no decipitive forces, other wise damping effect)
6.1.2. What defines a wave?
6.1.2.1. Amplitude and period
6.1.3. Key features:
6.1.3.1. amplitude (A):
6.1.3.1.1. is the maximum magnitude of displacement from equilibrium—that is, the maximum value of |x|. It is always positive. If the spring is an ideal one, the total overall range of the motion is 2A. The SI unit of A is the meter.
6.1.3.2. frequency (f):
6.1.3.2.1. is the number of cycles in a unit of time. It is always positive. The SI unit of frequency is the hertz
6.1.3.3. period (T):
6.1.3.3.1. is the time to complete one cycle. It is always positive. The SI unit is the second, but it is sometimes expressed as “seconds per cycle.”
6.1.3.4. angular frequency (ω):
6.1.3.4.1. is 2π times the frequency
6.1.3.4.2. Angular frequency ω= change in theta/t change in 2π/T change in 2πf
6.1.4. Horizontal Spring Mass system
6.1.4.1. Verbal explanations
6.1.4.1.1. At max compression/stretch -> |x| is maximum. F -> maximum so acceleration is maximum -> velocity is zero (when something is maximum its derivative is zero)
6.1.4.1.2. At equilibrium x=0, F is zero, Acceleration is zero, velocity is max since law of conservation of total mechanical energy
6.1.4.1.3. Restoring force and position are directly proportionate in magnitude but are opposite in direction
6.1.4.2. Equations
6.1.4.2.1. Force
6.1.4.2.2. Position
6.1.4.2.3. Velocity
6.1.4.2.4. Acceleration
6.1.4.2.5. Angular Frequency
6.1.4.2.6. Period
6.1.5. Vertical Spring Mass system
6.1.5.1. equations
6.1.5.1.1. Force
6.1.5.1.2. Position
6.1.6. Spring Mass systems in combination
6.1.6.1. n number of springs
6.1.6.1.1. Series
6.1.6.1.2. Parallel
6.1.7. Simple Pendulum
6.1.7.1. Characteristics:
6.1.7.1.1. - Point mass system - Massless frictionless string - angle <15 rad
6.1.7.1.2. In reality this is impossible to achieve since there are no massless strings and there is no such thing as a point particle
6.1.7.2. equations
6.1.7.2.1. Force
6.1.7.2.2. Angualr Frequency
6.1.7.2.3. Period
6.1.8. Physical Pendulum
6.1.8.1. Characteristics:
6.1.8.1.1. - Point mass system - Massless frictionless string - angle <15 rad
6.1.8.1.2. In reality this is impossible to achieve since there are no massless strings and there is no such thing as a point particle
6.1.8.2. equations
6.1.8.2.1. Force
6.1.8.2.2. Angualr Frequency
6.1.8.2.3. Period
6.1.9. Torsional Pendulum
6.1.9.1. characteristics
6.1.9.1.1. back and forth circular motion
6.1.9.2. equations
6.1.9.2.1. Force
6.1.9.2.2. Angualr Frequency
6.1.9.2.3. Period
6.1.10. Energy in SHM
6.1.10.1. 1/2Iω² = 1/2κθ²
7. Unit 7: Gravitation
7.1. Newton's law of Gravitation
7.1.1. Fg = Gm1m2 ---------- r^2
7.1.1.1. r
7.1.1.1.1. Distance from center to center
7.1.1.1.2. Unit: meters
7.1.1.2. G
7.1.1.2.1. Gravitational constant
7.1.1.2.2. Unit: Nm^2/kg^2
7.1.1.3. m
7.1.1.3.1. mass of object 1/2
7.1.1.4. Fg
7.1.1.4.1. force of gravity of 1 on 2/ 2 on 1
7.1.1.4.2. Newton's third law pairs
7.1.2. Any two objects of masses m1 and m2 at a distance r, from center to center, will undergo a mutual force of attraction Fg through the equation
7.1.3. F as a function of R (radius of massive body)
7.1.3.1. For solid sphere
7.1.3.1.1. area inside the sphere
7.1.3.1.2. outside the sphere
7.1.3.2. For hollow sphere
7.1.3.2.1. area inside the sphere
7.1.3.2.2. On or near the surface of the sphere
7.2. Gravitational Field Equation
7.2.1. finding baby g equation
7.2.1.1. g = Gm -------- r^2
7.2.2. experimentally we can use Force meter to determine Fg and diving it by m to find g
7.2.3. Any object with mass m and radius r, acts like a magnet to all objects.
7.3. Gravitational Potential Energy
7.3.1. Change in potential energy= -Work of force of gravity
7.3.2. Ug= - Gm1m2 ---------- r
7.4. Kepler and his laws
7.4.1. 1) All planetary orbits are ellipses
7.4.2. 2) The area covered in a specific amount of time, in an orbit is equal to every other area covered in that same amount of time
7.4.3. 3) T² = 4π²r³ ----- GM
7.5. Orbits
7.5.1. Apsis
7.5.1.1. Aphelion
7.5.1.1.1. furthest point on an orbit to the body
7.5.1.1.2. a away
7.5.1.2. Perihelion
7.5.1.2.1. closest point on an orbit to the body
7.5.1.2.2. p pclose
8. Mathematics in Physics
8.1. Calculus
8.1.1. Maximum Rule: A function is at its maximum when its derivative is equal to zero
8.1.2. Derivation:
8.1.2.1. https://www.math.ucdavis.edu/~kouba/Math17BHWDIRECTORY/Derivatives.pdf
8.1.2.2. https://cdn1.byjus.com/wp-content/uploads/2021/04/Differentiation-formulas-PDF.pdf
8.1.3. Integration
8.1.3.1. https://tutorial.math.lamar.edu/pdf/common_derivatives_integrals.pdf
8.1.4. Derivation + Integration (just another resource)
8.1.4.1. https://tutorial.math.lamar.edu/pdf/common_derivatives_integrals.pdf
8.1.5. All of Claculus
8.1.5.1. https://www.unit5.org/site/handlers/filedownload.ashx?moduleinstanceid=8312&dataid=14755&FileName=Calculus%20for%20AP%20Physics.pdf https://www.youtube.com/watch?v=oja-Oyg38XE Books: https://pup-assets.imgix.net/onix/images/9780691181318/9780691218786.pdf https://www.gutenberg.org/files/33283/33283-pdf.pdf
8.2. Dimensional Analysis
8.2.1. mathematical technique used to check and derive relationships between physical quantities by examining their units of measurement and converting them to length/time/mass.
8.3. Graph Analysis
8.3.1. The area under the line in an x y coordinate plane (starts at slope ends at x axis=0) is the product of x and y
8.3.2. slope of the graph represents delta x divided by delta y
8.3.3. https://youtu.be/nUb7xfkc0Ac?t=579
8.4. Trigonometry Rules https://www.youtube.com/watch?v=5zi5eG5Ui-Y
8.4.1. 2sinacosa = sin2a
8.4.2. cos(-a)=cosa
8.4.3. sin(-a)=-sin(a)
8.4.4. tan(-theta)=-tan(theta)
8.4.5. Lesson #1: Angles
8.4.5.1. Degree --> Radian *180/Pi Radian --> Degree * PI/180
8.4.5.1.1. Degrees
8.4.5.1.2. Radians