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### Physics

Lecture notes and guidelines used during times of my profession as a private tutor/lecturer.

## AP Physics Schedule

 Date Topics 8/20 (Wed.) Nuclear physics? - homework help 8/26 (Tue.) Motion - lab report planning 8/31 (Sun.) Kinematics - test review 9/2 (Tue.) Gravity - lab report 9/10 (Tue.) Universal Gravitation & Kepler's Laws - homework help 9/24 (Wed.) Optics - test review 9/29 (Mon.) Circular motion - test problems 10/10 (Fri.) Circular motion - lab report 10/14 (Tue.) Simple harmonic motion, Waves 10/21 (Tue.) Waves - homework problems 10/28 (Tue.) Waves - test review

## Harmonic motion

• Oscillating system - Any system that always experiences a force acting against the displacement of the system (restoring force).
• Restoring force - A force that always acts against the displacement of the system.
• Periodic Motion - Any motion in which a system returns to its initial position at a later time.
• Amplitude - The maximum displacement of an oscillating system.
• Period - The time it takes for a system to complete one oscillation.
• Frequency(Hz) - The rate at which a system completes an oscillation.
• Angular Frequency - The radian measure of frequency: ω = 2Πν = 2∏/T
• Simple Harmonic Motion - Any motion that experiences a restoring force proportional to the displacement of the system.
• ma = -kx

## Kinematics

• 1-D Motion
• Displacement: the shortest distance between two points: the origin and the displaced point
• Velocity: the rate of change in displacement with respect to time
• Acceleration: the rate of change in velocity with respect to time
• 2-D Motion
• Ignore air resistance
• Gravitational force law F = -mg
• Newton's 1st Law: law of inertia
Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
• An object that is not moving will not move until a net force acts upon it.
• An object that is in motion will not change its velocity (accelerate) until a net force acts upon it.
• Newton's 2nd Law: law of resultant force
The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

• Newton's 3rd Law: law of reciprocal actions
All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.
• Coefficient of friction μ = F/N
• Normal force: net force compressing two parallel surfaces together; direction is perpendicular to the surfaces

## Circular motion

• Newton’s Law of Universal Gravitation
Fg = G x m1m2 / r²
gravitational constant G = 6.67e-11 N*m²/kg²; me = 5.98e24 kg
• Uniform circular motion: occurs when a body moves in a circular path with constant speed
• Centripetal Acceleration: ac = v² / r
• Centripetal Force: T = mac = mv² / r
• Kepler's Laws
1. The path of each planet around the sun is an ellipse with the sun at one focus
2. A planet’s speed is relevant to its distance from the sun
3. Given the period(T) and semimajor axis(a) of a planet’s elliptical orbit, the ratio T²/a³ is the same for every planet
(T1/T2)² = (r1/r2
M = 4∏²r³/GT²

## Optics

### Lenses

• Focal point: point of convergence
• Lensmakers' Equation
f is the focal length of the lens,
n is the refractive index of the lens material,
R1 is the radius of curvature of the lens surface closest to the light source,
R2 is the radius of curvature of the lens surface farthest from the light source, and
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).

Convex lenses: converges at a single point

Concave lenses: causes parallel rays to diverge after passing through the lens

### Spherical mirrors

• Centre of curvature (C): located at the centre of an imaginary sphere with the same curvature as the mirror
• Radius of curvature (R): any straight line drawn from the centre of curvature to the curved surface
• Vertex (V): geometric centre of the actual curved mirror surface
• Principal axis (PA): any straight line passing through both vertex and the center of curvature
• Focal point (F): lies halfway between the center of curvature and vertex of the mirror
• Focal length f = R/2

Concave mirrors: hollowed inside surface

Convex mirrors: outside the sphere shape

Spherical aberration

## Kinematics Schedule

 Date Topics Assignment 9/15 (Mon.) Kinematics overview: Uniform motion Kinematics (ch.2-3) 9/16 (Tue.) Forces and Motion: Newton's 3 laws of motion Energy and Work overview Forces and Motion (ch.4) 9/18 (Thu.) Physics: Kinematics problem set Energy and Work: law of conservation of energy Momentum and Collision Energy and Work (ch.5-ch.6) 9/20 (Sat.) Physics: Work&Energy problem set Circular Motion and Gravitation Circular motion(ch.7)

## Kinematics

• Uniform motion: movement at a constant speed in a straight line
• Nonuniform motion: movement involves in speed and/or direction
• Base units and derived units
• Scalar quantity: magnitude only
• Instantaneous speed: speed at a particular instant
• Average speed = total distance / time
• Vector quantity: both magnitude and direction
• Position(d): distance and direction of an object from a reference point
• Displacement(Δd): change in position of an object in a given direction
• Resultant displacement(ΔdR) = Σ(Δd)
(Pythagorean theorem example)
• Velocity: rate of change in position
• Average velocity(ν) = Δd(change of position) / Δt(time interval)
• Acceleration: rate of change in velocity
• Instantaneous acceleration
• Average acceleration(a) = Δv(change of velocity)/Δt
• Calculus application
• Derivatives and integral
• calculation of uniform acceleration from position-time graph
• tangent technique
• Formula derivation
a = Δv / Δt
vf = vi + a*Δt
Δd = ½(vi+vf)Δt (integral)

Δd = viΔt + ½a(Δt)²

Δd = ½(vi+vf)(vf-vi)/a
Δd = (vf²-vi²)/2a

## Forces and Motion

• Force: simply push or pull
• Gravitational force: force of attraction between all objects in the universe
• mass: quantity of matter in an object
• weight: force of gravity on an object
• Law of Universal Gravitation: the force of gravitational attraction between any two objects is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between their centres.
FG = Gm₁m₂/d² G=6.67 x 10e-11 N*m²/kg²
• Normal force: force perpendicular to the surfaces of the objects in contact
• Friction = μ x FN
• static friction: force that tends to prevent a stationary object from starting to move
• kinetic friction: force that acts against an object's motion in a direction opposite to the direction of motion

#### Newton's First Law of Motion: the law of inertia

If the net force acting on an object is zero, the object will maintain its state of rest or constant velocity
1. Objects at rest tend to remain at rest (e.g. acceleration in moving vehicle)
2. Objects in motion tend to remain in motion (e.g. de-acceleration in moving vehicle)
3. If the velocity of an object is constant, the net external force acting on it must be zero.
4. If the velocity of an object is changing in either magnitude and/or direction, the change must be caused by a net external force acting on the object.
• Inertia: property of matter that causes a body to resist changes in its state of motion; directly proportional to the mass

#### Newton's Second Law of Motion

If the net external force on an object is not zero, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the object's mass

#### Newton's Third Law of Motion: action-reaction

For every action force, there is a reaction force equal in magnitude, but opposite in direction
e.g. Earth and an apple

## Energy, Work, Power

• Energy: capacity to do work
• Gravitational potential energy: possessed by an object because of its position relative to a lower position
Eg = FΔh = mgΔh
• Kinetic energy: energy due to the motion of an object
Ek = FΔd = maΔd = ½mv² (derivation)
• Thermal energy: energy in which temperature
• temperature: measure of the average kinetic energy of the substance
• Law of Conservation of Energy and Efficiency
When energy changes from one form to another, no energy is lost. (example problem)
• Efficiency = useful energy output / energy input (e.g. lightbulb - heat)
• Work:energy transferred to an object by an applied force over a measured distance (Joules = N x m)
W = FΔd
• Power:rate of doing work or transforming energy (Watts = J / t)
P = W/Δt= ΔE/Δt

## Momentum and Collision

• Momentum
p = mv
• Impulse
J = Δp = FΔt =
• Conservation of momentum: momentum stays constant
• Collision
• Elastic collision
• Inelastic collision

## Circular Motion

• Uniform circular motion: occurs when a body moves in a circular path with constant speed
• Centripetal Acceleration: ac = v² / r
• Centripetal Force: T = mac = mv² / r
• Newton’s Law of Universal Gravitation
Fg = G x m1m2 / r²
gravitational constant G = 6.67e-11 Nm²/kg²

### Physics: Work & Energy problem set

1. How much work does a person do in pushing a box with a force of 10 N over a distance of 4.0 m in the direction of the force?

2. A person pushes a 10 kg box at a constant velocity over a distance of 4 m. The coefficient of kinetic friction between the box and the floor is 0.3. How much work does the person do in pushing the box?

3. How much work does the force of gravity do in pulling a 10 kg box down a 30Âº inclined plane of length 8.0 m? Note that sin 30 = cos 60 = 0.500 and cos 30 = sin 60 = 0.866.

4. How much work does a person do in pushing a box with a force of 20 N over a distance of 8.0 m in the direction of the force?

5. A worker does 500 J of work on a 10 kg box. If the box transfers 375 J of heat to the floor through the friction between the box and the floor, what is the velocity of the box after the work has been done on it?

6. A person on the street wants to throw an 8 kg book up to a person leaning out of a window 5 m above street level. With what velocity must the person throw the book so that it reaches the person in the window?

7. A forklift lifts a crate of mass 100 kg at a constant velocity to a height of 8 m over a time of 4 s. The forklift then holds the crate in place for 20 s.

How much power does the forklift exert in lifting the crate?

How much power does the forklift exert in holding the crate in place?

Answer key: 1. 40J 2. 120J 3. 400J 4. 160J 5. 5 m/s 6. 10 m/s 7. 2.0 kW; 0W