Unit1_AnzaiM

__**Lesson 1: Introduction**__
Informational lesson to set up materials and resources needed for the course.toc

__**Lesson 2: Kinematics**__

 * Distance - how far you've traveled in total
 * Unit - Meter
 * Symbol - d
 * Type of Quantity - Scalar
 * Displacement - net/change in position relative to some __origin__(takes direction into account)
 * Unit - Meter
 * Symbol - d
 * Type of Quantity - Vector
 * Speed - rate of change of position
 * Unit - Meter/Second
 * Symbol - v
 * Type of Quantity - Scalar
 * Velocity - rate of change of position, based on displacement (takes direction into account)
 * Unit - Meter/Second
 * Symbol - v
 * Type of Quantity - Vector
 * Acceleration - how fast speed/velocity changes
 * Unit - Meter/Second^2 or Meter/Second/Second
 * Type of Quantity - Vector
 * Vector - a type of quantity that requires both quantity and direction
 * Scalar - a type of quantity that requires only quantity

__4 Types of Motion__


 * At rest - no motion, not moving
 * Constant velocity - no change in speed, covering same distance in same time
 * V(av) = (delta d) / (delta t) also used in instantaneous rate of change
 * Increasing velocity - starting slower and steadily getting larger/faster
 * Decreasing velocity - starting faster and steadily slowing

__Lab: Constant Speed__ June 27, 2011

__Objective:__ What does a graph of constant speed look like? __Hypothesis:__ It looks like a linear line. __Rationale:__ It looks like a linear line because, the rate at which distance traveled is constant to the rate of time. It can't have fluctuation in the graph, because it would not be constant. Also it can't have 0 slope because it would not have any velocity.

__Data:__ __Conclusion__: The graph of an object moving at a constant speed is a linear line. The line has a constant slope, which is rise/run or (delta distance / delta time) which is average speed the graph on the 2 slopes showed different slopes. The shallow graph had a slope of 1.0962, and the steeper graph had one that was 1.4621. The graph also showed an R^2 value which basically represents how close the graph is to a linear line. The shallow graph showed a R^2 value of 0.9967. The steeper graph showed a R^2 value of 0.9847. Because the R^2 value was near 1, it meant that there was little shift in data. Thus, the graph of an object moving at a constant speed is a linear equation with a slope that is not 0.

__**Homework: June 27, 2011**__
__Introduction to Kinematics:__
 * 1) What is the language of Kinematics?
 * 2) What exactly is the term Kinematics stand for?
 * 3) What is mechanics?
 * 4) How can we understand kinematics?
 * 5) What kind of terms does Kinematics have?

The language of kinematics is a system made to describe the science of motion in alternate forms such as:
 * words
 * diagrams
 * numbers
 * graphs
 * equations

It is most important to understand the material not through memorization, but rather contemplate information, thinking about its meaning and how it works.


 * 1) The language of kinematics is a system made to describe the science of motion in alternate forms.
 * 2) The science of describing motion.
 * 3) The study of motion of objects.
 * 4) To understand kinematics, we must understand the concept rather than memorizing the information.
 * 5) Kinematics includes: scalars, vectors, distance...etc.

__Scalars and Vectors:__

Mathematical quantities that are used to describe the motion of objects can be divided into two categories.
 * __Scalars__ - quantities that only require the numerical value
 * __Vectors__ - quantities that require both the numerical value and the direction

Check Your Understanding Answers: a) scalar b) vector c) vector d) scalar e) scalar f) scalar

__Distance and Displacement:__

The basic quantities in physics that express the movement or positions of a given object.

traveled. (How "out of place" an object is)
 * __Distance__ - a scalar quantity that describes the total movement or change of position by an object
 * __Displacement__ - a vector quantity that refers to the position of the object relative to the point of origin regardless to the distance

Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m). Yet when she is finished walking, she is not "out of place" - i.e., there is nodisplacement for her motion (displacement = 0 m). ([])

Quick Quiz 1: Distance traveled - (180 m + 140 m + 100 m) = 420 m Displacement - 140 m, to the right

Quick Quiz 2: Distance traveled - (35 yds + 20 yds + 40 yds) = 95 yds Displacement - 55 yds, to the left

Check Your Understanding Answers:
 * 1) The cross country team returns back to the school which is the point of origin so their displacement would be 0.
 * 2) The car would have a displacement of 0 if the finish line and starting line are the same.

__**Speed and Velocity:**__


 * __Speed__- a scalar quantity that defines how fast the object is gaining distance
 * __Velocity__ - a vector quantity that defines the rate of change of position based on displacement (takes direction into account)

When expressing speed and velocity, the main difference between the two would be that velocity requires a direction to be included for the data. An example would look like 25 km/hour, North. While information for speed would only require the 25 km/hour.

When calculations are made for speed and velocity there is both instantaneous, and average speed.
 * Instantaneous Speed - the speed at a specific time or position
 * Average Speed - the average distance traveled in a given amount of time

To get average speed you must use the formula: To get average velocity you must use the formula: Quick Quiz 1: Average Speed - 140m/min Average Velocity - 47.6m/min, to the right

Quick Quiz 2: Average Speed - 9.5m/min Average Velocity - 5.5m/min


 * __Acceleration:__**

A vector quantity that measures how the velocity is changing in regards to time.




 * __The Meaning of Shape for a p-t Graph:__**

Very important information can be derived from a position time graph. The position time graph is able to explain how the object is moving in regards to both distance and time. There are 4 key types of motion that could be understood from these graphs.

__4 Types of Motion__

> > - no change in speed, covering same distance in same time
 * At rest - no motion, not moving (from 5 to 10 seconds)
 * Constant velocity
 * V(av) = (delta d) / (delta t) also used in instantaneous rate of change
 * Increasing velocity - starting slower and steadily getting larger/faster
 * Decreasing velocity - starting faster and steadily slowing

__Describing Motion Time Graphs:__

Physics Slope Applet
 * __Interesting Relative Physics:__**

__**Lesson 3: Motion Diagrams June 28, 2011**__

 * qualitative representations
 * relative sizes and directions of velocity and acceleration

Motion Diagram Representation Don't let earlier conventions confuse your thinking in physics. Like the problem of no such thing as deceleration. For our class we are going to use the conventional signs of the graph axis.
 * at rest || v=0 || a=0 ||
 * constant || ->->-> || a=0 ||
 * increasing || . ->-->> || -> a ||
 * decreasing || ->--->--> || <- a ||

Motion Diagram Practice: 1) up ---> +v, down <--- -a 2) ---> +v, a = 0 3) ---> +v, ---> +a 4) -> --> ---> --> ->. -v, ---> -a

Ticker Tape Diagrams: x.......x..........x................x.........................x..................................x Increasing Speed

x....................x....................x...............x.......x......x....x..x.x Decreasing Speed

__Lab: Free Fall__

__Objective:__ What is acceleration due to gravity? __Hypothesis:__ 9.81 m/second^2 __Procedure:__ We started by receiving a strip of spark tape. Then we marked the top end of the tape to signify one side. We put the spark tape through the spark timer and attached a weight to the end of the spark tape. After turning on the spark timer, we dropped the weight to measure the acceleration of the object in free fall. Next we measured the distance between the origin or the first dot and the next dot. __Data Table:__



__Graph:__



__Analysis:__

The graph that I had created is relatively close to the value of gravity. My percent error comparative to the theoretical value of gravity was (|9.81 - 9.499| / 9.81) * 100 = 3.17023455 %. The class difference is (|9.08 - 9.499| /9.81) * 100 = 4.271151866%. This difference occurred due to the friction between the spark tape and the spark timer caused a slower rate of acceleration and drop. Also the air resistance occurring around the object could have caused the smaller value. Other than that the different starting points on the spark tape could have also caused a difference.

**__Homework June 28, 2011:__**
__Introduction to Diagrams:__

The use of diagrams in physics allows us to represent physical concepts into a visual representation. This helps those who learn with better with a visual representation as well as those who would like to see a more physical representation. Without this, we must use numerical properties such as negatives and positives to represent the motion of the objects.

There are several simple ways to attain a physical representation of physics.

__Ticker Tape Diagrams:__

A method that records the velocity of an object by creating marks at a specific rate. By doing so we can find whether the object is changing it's speed. This method can only record scalar quantities because it cannot specify the direction of the objects.

The Ticker Tape has been innovated by a spark tape timer. Instead of the carbon paper that it used, it is now replaced with a more accurate tape that is marked by electricity.



__Vector Diagrams:__

Is a visual representation that is able to show Vector quantities. The Vector diagrams are created by drawing arrows towards a specific direction. These arrows are able to represent both the direction and the speed at which an object is moving. When the arrows are smaller, they represent little speed. When it is stretched into a larger arrow it is considered to have faster/larger speed.



__The Meaning of Shape for Vector Time Graphs:__

Along with the use of words, diagrams, and numbers used to represent the motion of an object, graphs can be used as well. The specific features of the motion of objects are demonstrated by the shape and the slope of a line on a graph.

These graphs show different results

such as the one below: This graph represents an object with a constant velocity.

This graph represents an object with an increasing velocity: __The Meaning of Slope:__

Constant velocity motion and accelerated velocity motion can be represented by slopes. The slope on a vertical time graph is the same as the rate of acceleration. The slope on a position time graph is able to reveal very important information on a velocity time graph. Such information such as how the object will act in terms of velocity whether it be constant, accelerating, or at rest.

__Determining the Slope on the Vertical Time Graph:__

The slope on a Vertical Time Graph is considered to be the rate of acceleration. The slope equation says that the slope of a line is found by determining the amount of //rise// of the line between any two points divided by the amount of //run// of the line between the same two points. A method for carrying out the calculation is
 * 1) Pick two points on the line and determine their coordinates.
 * 2) Determine the difference in y-coordinates for these two points (//rise//).
 * 3) Determine the difference in x-coordinates for these two points (//run//).
 * 4) Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

__Introduction to Free Fall:__

Free falling is a concept in physics where an object is falling towards the earth by the sole influence of gravity.
 * Free-falling objects do not encounter air resistance.
 * All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for //back-of-the-envelope// calculations)

__The Acceleration of Gravity:__

9.8m/s/s is the acceleration for gravity. It can be used to calculate the acceleration.

__Representing Free Fall by Graphs:__

There are two types of graphs that can be used to represent free fall. The first would be the position time graph that would look like a graph with a steeper slope the farther it gets from the origin. The second would be the velocity time graph that would look like a linear graph.

__The Big Misconception:__

The big misconception is that people believe different objects have different forces of gravity. Because free fall does not include air resistance every object has equal acceleration towards the ground.

__The Kinematics Equations:__

The Kinematics Equations utilize displacement, velocity, and acceleration to create four essential formulas in physics.

__Kinematic Equations and Free Falling:__

The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps:
 * 1) Construct an informative diagram of the physical situation.
 * 2) Identify and list the given information in variable form.
 * 3) Identify and list the unknown information in variable form.
 * 4) Identify and list the equation that will be used to determine unknown information from known information.
 * 5) Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information.
 * 6) Check your answer to insure that it is reasonable and mathematically correct.

Physics Joke!

__Lesson 5: Newton's Laws__
1st Law Inertia
 * 1) An object at rest will stay at rest
 * 2) An object in motion will stay in motion
 * 3) Unless forced to do otherwise

1. At Rest = Static Equilibrium v = 0, a=0 Forces are Balanced

At constant speed in a straight line.

Galileo's Incline Experiment

2. v =/= 0 a = 0 Dynamic Equilibrium

__Mechanical Force:__


 * push or pull
 * external to system (object)
 * contact (1 exception)
 * CAN NOT be transferred or carried

4 TYPES OF FORCES:

Weight w, Fg - pull on earth on mass, points straight down w= m*g Friction f, Ff - 2 surfaces rub together, Friction points parallel to surfaces, opposite the direction of motion. Normal N, FN - "support" force, whenever two surfaces are in contact. perpendicular to the surface, it must go through the system. Tension T,FT - tension is only caused by rope or chain.

__Free Body Diagrams__:


 * Representation of all forces action on a system
 * All forces are shown with linear arrows + are labeled with symbols.

__**Lab: Newtons 2nd Law**__
__Objective:__ What is the relationship between a) Net Force and Acceleration of an object? b) Mass of object and its acceleration?

a) Acceleration will increase when net force increases. b) The greater the mass of an object the harder it is to accelerate because of static friction.

a) quadratic graph, it would look like a quadratic graph which increases by greater net force. The object remains constant but the force will apply more acceleration causing a quadratic graph. b) inverse, the greater the mass the less acceleration so the graph would look like an inverse graph

__Data Table 1:__

__Graph 1:__



__Data Table 2:__



__Graph 2:__



__Analysis:__ The theory derived from this lab was Newton's Second Law (acceleration = force / mass). Acceleration equals Force divided by mass. This can be derived from our first graph because our linear equation used a form of newton's second law: Force = mass * acceleration. On our graphs it showed the equation 0.548x + 0.0311. This shows us the validity of newton's equation because it can be applied to our experiment which directly tested the relationship between net force and acceleration. Also our second graph incorporated a form of newton's second law: Acceleration = Force / Mass. Our equation turned out as 0.2293/x^1.119. This again shows the validity of the equation because we tested the relationship between force and mass. Although the lab results were fairly good, there was problems that caused differences in our equations. The percent error to the theoretical values for the equation of graph 1 was, 3.396%. For the second graph it was 22% error. These errors came mainly from the friction involved in the movement of the cart as well as the friction by the pulley.

**__Homework: June 29, 2011__**
__Newton's First Law:__

Newton's First Law is sometimes regarded as the law of inertia. Newton's first law is a very popular phrase that most people hear within their lifetime.

"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

This simply means that Objects will keep doing what they are doing. An example would be if an object is in rest, then it would remain in rest. If an object was traveling 25mph, north, it would continue traveling 25mph, north. __Unless__ the object is acted upon by an unbalanced force.

__Galileo and the Concept of Inertia:__

Galileo a scientist in the seventeenth century composed an experiment that dealt with inertia. He proposed that object should move infinitely if there was no outside force causing it to hinder its movement.



__State of Motion:__

The state of motion can be defined by the velocity of an object whether it be at rest, increasing speed, decreasing speed, or constant. Inertia a key component of Newton's 1st Law and is defined as the ability for an object to maintain its velocity and acceleration without change.

__Balanced and Unbalanced Forces:__

If unbalanced forces are what causes objects to be removed from constant motion, what exactly is an unbalanced force? That is the question that has to be answered to understand Newton's 1st Law. When force is balanced, external forces balance each other out creating the effects of Newton's 1st Law. For example if a book was sliding to the left, it would receive unbalanced force to the right because of friction. Friction changes the state of motion, thus it is an unbalanced force that causes Newton's 1st Law to be inapplicable.

__The Meaning of Force:__

A force is a push or a pull on an object. There are two different types of forces

Contact Forces: Forces that result from direct contact on an object. Examples include, normal force, friction force, etc.

Action at a Distance Forces: Forces that result from a distance. An example would be the sun's gravitation force, the earth's gravitational force, on objects.

Force can be measured in Newtons, which are units that state the amount of force required to push or pull a 1kg object 1m/s. Although Force can be measured in Newtons, it is considered a Vector quantity and requires directional values.

__Newton's 1st Law Joke:__

__Lesson 6: Newton's 2nd Law__

To solve problems using newton's second law. First identify the force whether it is weight, friction, normal etc, Then get the mass and look at the problem. REMEMBER NET FORCE so you must take into account different forces that may cancel each other out.

__Lab: Friction Lab__

__Data:__ Locations: Average: Gym Floor 0.286 Concrete 0.486 Floor Tile 0.277 Table Top 0.205 Carpet 0.42 Pavement 0.358

__Work:__ __Analysis:__ From this lab we can understand the concept of the coefficient of friction. By testing out many surfaces by hand, we can understand that different surfaces behave differently in terms of friction. These tests were conducted by using a newton scale weight, and we found the friction at 0 acceleration. Thus friction was found. When Friction is found the coefficient value of friction can be found by dividing the force by the normal force of the object.

__Homework June 30, 2011__
__Newton's 2nd Law:__

The law states that net force is directly proportional to acceleration. Also that mass is indirectly proportional to acceleration.

__Finding Individual Forces and Acceleration:__

In order to find these important pieces of information, we must use Newton's second law and the equation for frictional force. By doing so we can find both the individual forces as well as the acceleration needed to solve most problems.

__Physics Joke:__

Q:WHY DID THE COW FALL OFF THE ROOF? A: BECAUSE THE COW DIDN'T HAVE ENOUGH MU (MOO)! __Lesson 9:__

3rd Law: Every Action has an equal but opposite reaction All forces come in pairs, that equal in size, pointing in opposite directions, acting on 2 separate systems.

Apparent weight.

__Drop and Pull Challenge Problem:__

How much mass did we have to hang in order to get a 500g cart to move 0.8 meters in 2.1 seconds?

We were given the values of the mass of the cart and the distance it had to move in a certain amount of time. In order to change the outcome of the time we had to deal with the value of time.

Results: 2.12 seconds 2.16 seconds 2.10 seconds

Percent Error: 1.2698%

Work:

Causes of Errors: The initial velocity may have not been 0 when the cart started to move out of its origin. Problems such as friction and air resistance may have been problems that caused the errors as well. Also an accurate amount of mass wasn't available for our theoretical mass.

__**Homework: July 5, 2011**__
Method #2: __Air Resistance:__

Air resistance is the result of an object colliding with the air particles while above the ground. There are two common factors that effect the effects of air resistance. 1. The speed of the object 2. The total surface area of the object.

Air resistance always reaches a magnitude that causes terminal velocity. This means that the velocity of the falling object becomes 0. It is no longer accelerating but is falling at a constant rate.

__Two Body Problems:__ Two object problems, are those that have two objects connected to each other whether it be tension, normal force, or etc. To approach these kinds of problems we can take different steps to do so. Usually these problems consider an unknown such as acceleration.

__Newton's Third Law:__

For every action, there is an equal and opposite reaction. Forces always come in pairs. These pairs come with certain roles. One of the object is the reaction and one is the action. A good example is a fish that propels itself through water. It is able to move forward by recieving a reaction by the water. The force that the fish exerts on the water, it recieves back and gets forward momentum.

__Identifying Action and Reaction Force Pairs:__

Stated above.

__Vectors and Directions:__

The fact that forces are vectors, means that there is a need for a directional value.

In order to give these directional values, we are able to give descriptions such as east, northeast, west southwest, south, etc. Also we can give directional values by providing angles.

Also when describing vectors through free body diagrams or an axes, we can represent the magnitude and angle by how long and what angle the line is at.

__Vector Addition:__

When vectors are facing opposite to each other it is easily solved by adding the opposite values, one being negative and one positive. Same goes for vectors facing the same direction. When there are two vectors that create a right angle, the values can be solved through the Pythagorean theorem.

__Resultant:__

The resultant is just the result, or the sum of two or more vectors.

__Vector Components:__ Because often when we are given only a diagonal value off of the x and y axis, we are unable to figure out the two seperate forces of each axis. in order to figure these values out correctly we must be able to understand trigonometry to derive values from the original diagonal force.

__Vector Resolution:__

There are specific methods to develop the Vector Resolution. The steps that are provided on the physics classroom page is very good.

The method of employing trigonometric functions to determine the components of a vector are as follows:
 * 1) Construct a //rough// sketch (no scale needed) of the vector in the indicated direction. Label its magnitude and the angle that it makes with the horizontal.
 * 2) Draw a rectangle about the vector such that the vector is the diagonal of the rectangle. Beginning at the tail of the vector, sketch vertical and horizontal lines. Then sketch horizontal and vertical lines at the head of the vector. The sketched lines will meet to form a rectangle.
 * 3) Draw the components of the vector. The components are the //sides// of the rectangle. The tail of each component begins at the tail of the vector and stretches along the axes to the nearest corner of the rectangle. Be sure to place arrowheads on these components to indicate their direction (up, down, left, right).
 * 4) Meaningfully label the components of the vectors with symbols to indicate which component represents which side. A northward force component might be labeled Fnorth. A rightward force velocity component might be labeled vx; etc.
 * 5) To determine the length of the side opposite the indicated angle, use the sine function. Substitute the magnitude of the vector for the length of the hypotenuse. Use some algebra to solve the equation for the length of the side opposite the indicated angle.
 * 6) Repeat the above step using the cosine function to determine the length of the side adjacent to the indicated angle.

__Vector Addition:__ Again just like in the vector resolution, the vector addition or the diagonal angle can be figured out through the use of the Pythagorean theorem.

**__Lesson: July 5, 2011__**
Ground to Ground is 0 displacement on the y axis.

**__Lab: Projectiles in motion__**
__Part A:__ Projectiles: x and y axis are independent

Initial Height: 77.8

Distance from the initial launch to the landing point: 41.5 41.5 41.4 41.4 40.8 42.3 42.2 42.8

avg distance = 41.7375

Photogate Time .0135 .0135 .0145 .013

Avg Time / distance between photogates (1.6cm) = 1.11 m/s

Work for Part A: Part B: Work

We figured out the information by using the equation d = vot + 1/2(-9.8)t^2). By using the distances we could find the angle and find the individual velocity of the x and y component. We had experimental error because the photogate timers could have been before the object was in the path of a projectile. Also friction could have reduced the velocity before the initial launch of the object which could have changed our experimental values.

__**Homework: July 6, 2011**__

__What is a projectile?:__

2 Concepts I understood well within the "what is a projectile?" section. One is that vertical acceleration does not affect horizontal movement of an object. The second concept is that I understood the full definition of a projectile. A projectile does not have any other force than weight.

I read that an object must have no acceleration horizontally, which cleared up my definition of a projectile which is an object in motion with no horizontal acceleration and only vertical acceleration due to gravity.

__Characteristics of a Projectile's Trajectory:__ 1. Horizontally launched projectiles have the same air time no matter how fast the object is moving at the initial velocity. When an object is launched vertically, and changed in degrees, the horizontal velocity effects how long the object will stay in the air. 2.This table cleared up my understanding of the characteristics of a projectile's trajectory. 3. 4.
 * **Horizontal****Motion** || **Vertical****Motion** ||
 * Forces (Present? - Yes or No)(If present, what dir'n?) || No || YesThe force of gravity acts downward ||
 * Acceleration (Present? - Yes or No)(If present, what dir'n?) || No || Yes"g" is downward at 9.8 m/s/s ||
 * **Velocity** (Constant or Changing?) || Constant || Changing(by 9.8 m/s each second) ||

__Describing Projectiles with Numbers:__ 1. Projectiles have both horizontal and vertical values that change the motion of the objects. Each of the quantitative values are independent of each other. 2. I understood that if one of the values reduces or increases the overall velocity or speed of both axes become affected. The speed can be figured out through the Pythagorean theorem. 3. 4.

__Initial Velocity Components:__ 1. It is very important to distinguish the differences between initial velocity of each axes. We can figure out initial velocity through the use of trigonometry. 2. 3. 4.

__Horizontally launched practice problems:__ 1. The ways to approach the problem are simple. It is like any other problem but we must deal with trigonometry if the unknown is the initial velocity or speed. If we want distance or time we simply use d = vot + 1/2(a)(t^2) 2. 3. 4.

__Cool Picture:__ Very similar to the set up we had in class!

What is the relationship between acceleration of an object and angle of the incline?

__Hypothesis:__ It is a linear relationship.

__Objective:__ What is the relationship? The relationship is a linear relationship where the slope is the gravitational force of 9.8 m/s/s.

__Data and Graph:__

__Analysis:__ The angles could have changed as the cart hit the end of the tracks. The slope was supposed to be 9.8 m/s^2 because gravity is the only force acting upon it. Also there could reaction time errors that could have caused bad information,

**__Homework: July 7, 2011__**
Method #2 Headlining:

__Addition of Forces:__

The addition of forces in this concept deals with a force that has both horizontal and vertical features. When we use lab equipment such as a forceboard we can measure angled values easily by getting the force values from each chain branching off of the central object.

__Resolution of Forces:__

The horizontal forces that we have understood from previous lessons has given us information that it is both the vertical and horizontal forces. By using trigonometric functions we can apply it to angled force and use it in a manner that allows us to figure out each individual force.

__Equilibrium and Statics:__

Equilibrium/static forces implies that the object is either at rest or is at a constant motion or speed. When these qualities are met, their are specific qualities to the forces that are applied to the object. These special qualities is that the opposite forces from either angled or perpendicular, parallel forces cancel each other out. This keeps all unbalanced forces off of the object and keeps it in a equilibrium or static state.

__Inclined Planes:__

When dealing with inclined planes there are two different scenarios or motion paths that the object can take. The object can be either static from friction or in motion. Generally the deciding factor in inclined planes is the weight force. The off axis weight force causes the object to either move or remain static.

__Two Body Problems:__

A like to the problems for one dimensional two body problems, we must treat the objects as separate systems or a whole system. The objects must be understood just like a one body problem but we must also understand the interactions between the two objects.

__Newton's Law of Universal Gravitation:__

As the greatest physician in history Isaac Newton figured out that the force of gravity was directly proportional to the value of mass1 * mass2/ d^2. In order to set these two values, force of gravity and the values derived from the maths, Henry Cavendish came up with the constant from __The value of little g:__

The value of the gravitational constant on the surface of the earth 9.8m/s^2 was derived directly from Cavendish' formula.
 * === Location === || === Distance from ===

Earth's center (m)
|| === Value of g ===

m/s2
|| As we can see the values of g, on earths surface is figured out to be 9.8. As we move farther away from the earth, the force of gravity becomes smaller and smaller, but never reaches 0.
 * Earth's surface || 6.38 x 106 m || 9.8 ||
 * 1000 km above surface || 7.38 x 106 m || 7.33 ||
 * 2000 km above surface || 8.38 x 106 m || 5.68 ||
 * 3000 km above surface || 9.38 x 106 m || 4.53 ||
 * 4000 km above surface || 1.04 x 107 m || 3.70 ||
 * 5000 km above surface || 1.14 x 107 m || 3.08 ||
 * 6000 km above surface || 1.24 x 107 m || 2.60 ||
 * 7000 km above surface || 1.34 x 107 m || 2.23 ||
 * 8000 km above surface || 1.44 x 107 m || 1.93 ||
 * 9000 km above surface || 1.54 x 107 m || 1.69 ||
 * 10000 km above surface || 1.64 x 107 m || 1.49 ||
 * 50000 km above surface || 5.64 x 107 m || 0.13 ||

__Joke:__



Cool image:

__**Lab: Vertical Circles**__
Data: All Work: Analysis: Our experimental values are far off from the theoretical values because, we cannot accurately time our rotations, as well as count how many that we had. Also, it is extremely hard to reach a maximum velocity for several revolutions without it breaking. That is why we couldn't reach the maximum velocity. Also it is hard to maintain the slowest possible velocity without the weight to move towards the center of the circular motion. It is hard to keep it at a constant speed as well.

What happens to the period when you increase the radius of a conical pendulum? The periods become shorter as the radius of the conical pendulum increases.

Average periods: 10cm: 3.315s velocity: 3.259s percent error: 2 20cm: 3.291s velocity: 3.27s percent error: 0.6% 40cm: 3.277s velocity:3.24s percent error: 0.9% 60cm: 3.287s velocity: 3.218s percent error: 2% 100cm: 3.16s velocity: 3.14s percent error: 0.5%

Work:

Analysis: The lab showed great results, but there were some experimental errors. This is because reflex of the timer as well as the correct starting and stopping location of 1 revolution. Also the pendulum could have been creating an elliptical figure instead of the perfect circle which could have thrown off the times.

__Homework: July 7, 2011__
Questions: 1. How can we find average speed for circular motion? 2. How does acceleration in circular motion differ from 1 dimensional acceleration? 3. What exactly is centripetal force? 4. Why doesn't centrifugal force make sense? 5. How can we solve centripetal motion equations?

__Average Speed:__

1. How can we calculate average speed in a circular motion? The calculation of the average speed of a normal object moving horizontal can be calculated easily with delta distance over time. In terms of circular movement, average speed is fairly different. Because it moves in a circular motion, we have to find the distance by using circumference over time instead of the horizontal distance.

__Acceleration:__

When it comes to acceleration dealing with circular motion, many students make the error by saying that when an object is traveling at a constant speed in a circle they have an acceleration of 0. But this is not the case because acceleration is a vector and requires directional value. Because circular motion has constant change in direction, it does not have a constant acceleration.

__The Centripetal Force:__

Centripetal force is the force that pulls an object to the center of a circle. **Work = Force * displacement * cosine (Theta)**

The formula tells us that there is always force pulling the object closer to the middle of the circle. This steady force is what creates the existence of centripetal force.

__Misconception of Centrifugal:__

There are many students that make this error simply because it sounds similar, or of the theory behind it. Centrifugal theory states that when an object is moving in a circular direction, it is moving outwards away from the center of the circle. This is incorrect because the object is pulled towards the middle of the circle. It may seem like centrifugal is correct because when we ride rollercoasters and go through a circular motion, it feels as if our body is moving outwards away from the center of the circle, but it is just the law of inertia that is tricking the mind into believing that centrifugal force is what causes circular motion.

__Mathematics of Circular Motion:__

The mathematics behind circular motion is simple. It is the same application of newtons second law Force = mass * acceleration, but acceleration is different for circular motion. It is fairly similar in steps to solving the circular motion problems.

__Application of Circular Motion:__

We can use the formulas and information on circular motion by applying it to situations such as the circular motion of a car, a conical pendulum, and etc. When we use the formulas, we must take in to account that newton's second law is used with a difference in the acceleration.

__Joke:__