## 1. Measurement

### 1.1. Fundamental Units

1.1.1. Length (meter) Mass (kilogram) Time (second) Electric current (ampere) Thermodynamic temperature (kelvin) Amount of substance (mole) Luminous intensity (candela)

### 1.2. Derived Units

1.2.1. Many other quantities can be derived out of the combination of the basic quantities. For instance a speed is the ratio of a length by a time. Acceleration is the ratio of a speed by a time. And a force is the multiplication of acceleration by mass.

### 1.3. Trigonometry

1.3.1. Equations for trigonometric functions for a right triangle are sine, cosine, and tangent.

1.3.1.1. EQUATIONS

1.3.1.1.1. Add picture of right triangle here

1.3.2. Pythagorean Theorem

1.3.2.1. EQUATION

1.3.2.1.1. (c) is the hypotenuse of the triangle and (a) and (b) are its other two sides.

### 1.4. Significant Figures

1.4.1. Significant digits, also often called significant figures, represent the accuracy with which you know your values.

1.4.1.1. When you multiply or divide numbers, the result has the number of significant digits that equals the smallest number of significant digits in any of the original numbers.

1.4.1.1.1. So if you want to figure out how fast the skater was going, you divide 10.0 by 7.0, and the result should have only two significant digits — 1.4 meters per second.

1.4.1.2. When you’re adding or subtracting numbers, the rule is that the last significant digit in the result corresponds to the last significant digit in the least accurate measurement.

### 1.5. Metric Prefixes

1.5.1. PUT CHART OF METRIC PREFIXES HERE

### 1.6. Scientific Notation

1.6.1. The way that scientists easily handle very large numbers or very small numbers.

1.6.1.1. Example : 700 = 7 x 10^2

## 2. Vectors

### 2.1. Scalars

2.1.1. Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

2.1.1.1. Examples : Time, volume, speed, and temperature.

### 2.2. Vectors

2.2.1. Vector Addition

2.2.1.1. The operation of adding two or more vectors together into a vector sum.

2.2.1.1.1. PICTURE OF EXAMPLE

2.2.2. Vector Components

2.2.2.1. When you break a vector into its parts, those parts are called its components.

2.2.2.1.1. Example : In the vector (4, 1), the x-axis (horizontal) component is 4, and the y-axis (vertical) component is 1.

2.2.3. DIsplacement Vector

2.2.3.1. Displacement vector is a vector which gives the position of a point with reference to a point other than the origin of the coordinate system.

2.2.4. Unit Vector

2.2.4.1. A vector that has a magnitude of one.

2.2.4.1.1. FORMULA

2.2.5. Definition

2.2.5.1. Vectors are quantities that are fully described by both a magnitude and a direction.

2.2.5.1.1. Examples : Increase/Decrease in temperature, velocity, and force vector.

## 3. Kinematics

### 3.1. Speed

3.1.1. Speed (a scalar quantity) is the rate at which an object covers distance. The average speed is the distance (a scalar quantity) per time ratio.

3.1.1.1. FORMULA

### 3.2. Velocity

3.2.1. Velocity is defined as a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object.

3.2.1.1. FORMULA

3.2.2. The scalar (absolute value) magnitude of the velocity vector is the speed of the motion.

### 3.3. Acceleration

3.3.1. Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

3.3.1.1. FORMULA

### 3.4. Free Fall

3.4.1. A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall.

3.4.1.1. FORMULA

### 3.5. Instantaneous Velocity / Acceleration

3.5.1. Instantaneous Velocity

3.5.1.1. The velocity of an object in motion at a specific point in time.

3.5.1.1.1. FORMULA

3.5.2. Instantaneous Acceleration

3.5.2.1. The acceleration of the moving body at any instant of time is defined as its instantaneous acceleration.

3.5.2.1.1. FORMULA

### 3.6. Constant Acceleration

3.6.1. Constant acceleration is the special case of acceleration. When a moving body changes its velocity by the equal amount per second, the body is said to be moving with the constant acceleration.

3.6.1.1. Kinematic Equations

3.6.1.1.1. INCLUDE PICTURE OF FORMULAS

### 3.7. Acceleration in Gravity

3.7.1. The acceleration for any object moving under the sole influence of gravity.

3.7.1.1. g = G*M/R^2, where g is the acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is distance. The remainder of this lesson develops this formula, provides further explanation of its meaning, and shows practical examples of its use in calculating acceleration due to gravity.

## 4. Force and Motion

### 4.1. Force

4.1.1. In physics, a force is any interaction that, when unopposed, will change the motion of an object.

4.1.1.1. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.

4.1.1.1.1. Equation

4.1.1.2. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

### 4.2. Weight

4.2.1. The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg.

4.2.1.1. Since the weight is a force, its SI unit is the newton. Density is mass/volume.

### 4.3. Newton's Laws

4.3.1. Newton´s First Law

4.3.1.1. States that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

4.3.2. Newton´s Second Law

4.3.2.1. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

4.3.2.1.1. F = ma

4.3.3. Newton´s Third Law

4.3.3.1. All forces in the universe occur in equal but oppositely directed pairs.

### 4.4. Friction

4.4.1. Static Friction

4.4.1.1. Static friction is the friction that exists between a stationary object and the surface on which it's resting.

4.4.2. Kinetic Friction

4.4.2.1. Kinetic friction, also known as sliding friction or moving friction, is the amount of retarding force between two objects that are moving relative to each other.

4.4.2.1.1. helpful junk : http://study.com/academy/lesson/coefficient-of-kinetic-friction-definition-formula-examples.html

### 4.5. Inclined Plane

4.5.1. We refer to tilted surfaces as inclined planes. As an object travels down an inclined plane, the normal force acting on it also tilts because the normal force is a force perpendicular to the surface.

4.5.1.1. Picture of Inclined Plane

### 4.6. Mass

4.6.1. Mass is a measurement of how much matter is in an object. Mass is a combination of the total number of atoms, the density of the atoms, and the type of atoms in an object.

4.6.1.1. Mass is usually measured in kilograms which is abbreviated as kg.

## 5. Motion in a Plane

### 5.1. Uniform Circular Motion

5.1.1. Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction.

5.1.1.1. EQUATIONS

### 5.2. Centripetal Acceleration

5.2.1. Centripetal acceleration is the rate of change of tangential velocity.

5.2.1.1. FORMULA

### 5.3. Centripetal Force

5.3.1. A force that acts on a body moving in a circular path and is directed toward the center around which the body is moving.

5.3.1.1. FORMULA

### 5.4. Projectile Motion

5.4.1. Vertical Motion of a Projectile

5.4.1.1. There is a vertical acceleration caused by gravity; its value is 9.8 m/s², down, The vertical velocity of a projectile changes by 9.8 m/s each second

5.4.2. Horizontal Motion of a Projectile

5.4.2.1. The horizontal velocity of a projectile is constant

5.4.3. A projectile is any object that is given an initial velocity and then follows a path determined entirely by gravity.

5.4.3.1. Picture of arch thing

### 5.5. Newton´s Law of Gravitation

5.5.1. States that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

5.5.1.1. FORMULA

### 5.6. Kepler´s Laws

5.6.1. The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

5.6.2. An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)

5.6.3. The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

5.6.4. http://www.physicsclassroom.com/class/circles/Lesson-4/Kepler-s-Three-Laws

### 5.7. Motion of Satellites

5.7.1. First, an orbiting satellite is a projectile in the sense that the only force acting upon an orbiting satellite is the force of gravity. Most Earth-orbiting satellites are orbiting at a distance high above the Earth such that their motion is unaffected by forces of air resistance.

## 6. Work and Energy

### 6.1. Work

6.1.1. Work Definition - Work is done when a force that is applied to an object moves that object. The work is calculated by multiplying the force by the amount of movement of an object (W = F * d).

6.1.1.1. Example - A force of 10 newtons, that moves an object 3 meters, does 30 n-m of work.

### 6.2. Energy

6.2.1. Kinetic Energy

6.2.1.1. Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy.

6.2.1.1.1. Equation - KE = 0.5 • m • v2 where m = mass of object v = speed of object

6.2.2. Potential Energy

6.2.2.1. Potential energy is the energy that is stored in an object due to its position relative to some zero position. An object possesses gravitational potential energy if it is positioned at a height above (or below) the zero height.

6.2.3. Gravitational Energy

6.2.3.1. Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object

6.2.3.1.1. PEgrav = mass • g • height PEgrav = m *• g • h

6.2.4. Energy Definition

6.2.4.1. Energy is defined as the capacity of a physical system to perform work. However, it's important to keep in mind that just because energy exists, it doesn't means it's necessarily available to do work.

6.2.4.2. The SI unit of energy is the joule (J) or newton-meter (N * m). The joule is also the SI unit of work.

6.2.4.3. FORMS OF ENERGY

6.2.4.3.1. Kinetic Energy - Kinetic energy is energy of motion. A swinging pendulum has kinetic energy.

6.2.4.3.2. Heat - Heat or thermal energy is energy from the movement of atoms or molecules. It may be considered as energy relating to temperature.

6.2.4.3.3. Potential Energy - This is energy due to an objects position. For example, a ball sitting on a table has potential energy with respect to the floor because gravity acts upon it.

6.2.4.3.4. Mechanical Energy - Mechanical energy is the sum of the kinetic and potential energy of a body.

6.2.4.3.5. Light - Photons are a form of energy.

6.2.4.3.6. Electrical Energy - This is energy from the movement of charged particles, such as protons, electrons, or ions.

6.2.4.3.7. Magnetic Energy - This form of energy results from a magnetic field.

6.2.4.3.8. Chemical Energy - Chemical energy is released or absorbed by chemical reactions. It is produced by breaking or forming chemical bonds between atoms and molecules.

6.2.4.3.9. Nuclear Energy - This is energy from interactions with the protons and neutrons of an atom. Typically this relates to the strong force. Examples are energy released by fission and fusion.

6.2.4.3.10. Other forms of energy may include geothermal energy and classification of energy as renewable or nonrenewable.

6.2.5. Spring Potential Energy (Elastic Potential Energy)

6.2.5.1. Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc.

6.2.5.1.1. PEspring = 0.5 • k • x2 where k = spring constant x = amount of compression (relative to equilibrium position)

### 6.3. Power

6.3.1. Power is the rate of doing work. It is the amount of energy consumed per unit time. Having no direction, it is a scalar quantity. In the SI system, the unit of power is the joule per second (J/s), known as the watt in honour of James Watt, the eighteenth-century developer of the steam engine.

6.3.1.1. Equation : Power = Work / time

### 6.4. Conservation of Mechanical Energy

6.4.1. Conservation of mechanical energy states that the mechanical energy of an isolated system remains constant without friction.

6.4.2. The conservation of mechanical energy can be written as "KE + PE = const".

### 6.5. Work - Energy Theorem

6.5.1. The work-energy theorem states that the work done by all forces acting on a particle equals the change in the particle's kinetic energy.

6.5.1.1. Equation : The work W done by the net force on a particle equals the change in the particle's kinetic energy KE: W=ΔKE=12mvf2−12mvi2 .

6.5.2. The work-energy theorem can be derived from Newton's second law.

## 7. Momentum

### 7.1. Momentum

7.1.1. Momentum Definition

7.1.1.1. The quantity of motion that an object has.

7.1.2. Momentum Formula

7.1.2.1. Momentum = mass • velocity In physics, the symbol for the quantity momentum is the lower case p. Thus, the above equation can be rewritten as p = m • v

7.1.3. Conservation of Momentum

7.1.3.1. Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system.

7.1.3.1.1. FORMULA

### 7.2. Impulse-Momentum Change

7.2.1. In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. The product of mass and velocity change is known as momentum change. In a collision the impulse encountered by an object is equal to the momentum change it experiences.

7.2.1.1. Impulse = Momentum Change F • t = mass • Delta v

### 7.3. Collisions

7.3.1. Elastic Collisions

7.3.1.1. A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision.

7.3.2. Inelastic Collisions

7.3.2.1. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision.

### 7.4. Center of Mass

7.4.1. The center of mass (CM) of an object is a point that is the average or mean location of its mass, as if all the mass of the object was concentrated at that point. A uniform sphere has its center of mass at its geometric center. The CM is sometimes called the barycenter.

7.4.1.1. Formula : http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html

## 8. Rotation

### 8.1. Angular Measurement and Velocity

8.1.1. Angular Velocity

8.1.1.1. The rate of change of angular position of a rotating body.

8.1.1.1.1. Picture of Angular Velocity Formulas

8.1.2. Angular Measurement

8.1.2.1. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees. The SI unit of solid angle measurement is the steradian.

8.1.2.1.1. Picture

### 8.2. Angular Acceleration

8.2.1. Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha (α).

8.2.1.1. PICTURE

8.2.1.1.1. α = angular acceleration, (radians/s2) Δω = change in angular velocity (radians/s) Δt = change in time (s) ω1 = initial angular velocity (radians/s) ω2= final angular velocity (radians/s) t1 = initial time (s) t2= final time (s)

### 8.3. Rotational Kinematics

8.3.1. Rotational kinematics investigates lows of motion of objects along circular path without any reference to forces that cause the motion to change.

8.3.1.1. FORMULAS

### 8.4. Torque

8.4.1. Torque is the tendency of a force to cause or change the rotational motion of a body. It is a twist or turning force on an object. Torque is calculated by multiplying force and distance. It is a vector quantity, meaning it has both a direction and a magnitude. Either the angular velocity for the moment of inertia of an object is changing, or both.

8.4.1.1. FORMULA

### 8.5. Moment of Inertia

8.5.1. Moment of Inertia (Mass Moment of Inertia) - I - is a measure of an object's resistance to change in rotation direction.

8.5.1.1. I = m r^2 where : I = moment of inertia (kg m2, slug ft2) m = mass (kg, slugs) r = distance between axis and rotation mass (m, ft)

8.5.2. Moment of Inertia of a body depends on the distribution of mass in the body with respect to the axis of rotation

8.5.3. Moment of Inertia has the same relationship to angular acceleration as mass has to linear acceleration.

### 8.6. Rotational Kinetic Energy

8.6.1. The kinetic energy of rotation of a rigid body is obtained by first dividing it up into a collection of smaller masses, and then summing up the kinetic energies due to the tangential velocities of the individual masses making up that rigid body.

8.6.1.1. FORMULA : http://theory.uwinnipeg.ca/physics/rot/node6.html

8.6.2. The units of rotational kinetic energy are Joules (J).

8.6.3. When considering the total mechanical energy of a rigid body, this kinetic energy must be added to the kinetic energy of translation

8.6.3.1. FORMULA : http://theory.uwinnipeg.ca/physics/rot/node6.html

### 8.7. Angular Momentum

8.7.1. The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity.

8.7.1.1. FORMULA : http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

### 8.8. Conservation of Angular Momentum

8.8.1. The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.

8.8.1.1. https://www.boundless.com/physics/textbooks/boundless-physics-textbook/rotational-kinematics-angular-momentum-and-energy-9/conservation-of-angular-momentum-86/conservation-of-angular-momentum-328-11269/