Motion Test Review

1.1: Fundamental Physical Quantities

• Space, time, and matter are the three basic aspects of the material universe that we must describe and quantify in various ways in physics; all physical quantities involve measurements of space, time, and the properties of matter.
• Distance (space), time (time) and mass (matter) are the units of measure through which we quantify the material universe's three basic aspects; they are known as fundamental physical quantities.  It is difficult to define them because they are extremely basic concepts, especially time.
• Distance represents a measure of space in one direction; length, width, and height are distance measurements.
• Area (square units) and volume (cubed units) are physical quantities that are closely related to distance.
  

  

  These are the common units used for measuring distance.

• Time is a measure based on periodic phenomena; processes that repeat over and over at a regular rate.
• The rotation of the Earth was used to establish the universal unit of time (second); it takes Earth 86,400 seconds to rotate.
• To keep time we need something that cycles, swings, or oscillates at a constant rate.
• The units for time are universal; the Metric and English systems share them.

  

  These are the universal units used to measure time.

• Mass is a measure of how much matter an object contains.
• Mass is a measure of inertia; the larger the mass of an object, the greater its inertia and the more difficult it is to speed up or slow down.
• In the English system, weight is used instead of mass (even though it is not the same), that is why we may have never heard of the unit before.
  
  
• There are many units in each system because measurements are taken in very different scales; it's easier to use a unit that is to scale with the measurement being taken to end up with manageable numbers.
• Clocks measure time by using a process that repeats.
• Mechanical clocks use a swinging pendulum that swings back and forth at a steady rate and controls the hands on the clock's face.
• Mechanical wristwatches and stopwatches use an oscillating balance wheel that serves a pendulum's purpose.
• Quartz electric clocks and digital watches use regular vibrations of an electrically stimulated crystal made of quartz to keep time.
• The first step in designing a clock is to determine how much time it takes for one cycle of the oscillation (period); the clock's hands are set to rotate according to this.
• The time for one complete cycle of a process that repeats is called a period (T); it's a time measurement (its units are seconds, minutes...).
• You can also look at this by calculating the frequency, which is how many cycles take place before 1 second passes; for example, a pendulum's frequency may be 1/2 cycle per second.
• A pendulum consists of a weight dangling on the end of a string; it swings back and forth and we can use it to determine period and frequency.
• The period of the pendulum gets longer when the length of the string increases, and vice-versa.
• Earth's rotation is not strictly constant, so the universal time measure has been changed several times in seek of a more accurate second.
• The Earth-Sun system was used to tell time up until 1956; a second was defined as 1/86,400 of a mean solar day.
• In the late 1950s, the system was changed to ephemeris seconds that began in January of 1900.  These were based on the motion of Earth around the Sun and governed by Newton's laws of motion.
• In 1967, the atomic second was defined using oscillations of light waves given off by isolated cesium atoms.
• In the early 1970s the French Bureau International de l'Heure, the world's official timekeepers, introduced Coordinated Universal Time (UTC); the duration of the second is dictated by atomic time but is required to remain within 0.9 seconds of mean solar time.  Leap seconds are added or subtracted to compensate for changed in the rate of Earth's rotation.
• AM radio stations' frequencies are expressed in kilohertz (kHz); FM stations' are in megahertz (MHz).
• Kilo- is the metric prefix signifying 1 thousand; mega- is the metric prefix signifying 1 million.
• Giga- is another metric prefix that signifies 1 billion.  It is used with hertz when determining data like the speed of a computer's processor.

1.2: Speed and Velocity

• Speed is the rate of movement; it's a key concept to use when quantifying movement.  The two aspects of speed are:
• Speed is relative.
• The speed of a person running towards the front on the deck of a cruise ship that is going 20mph may be 8mph in relation to the cruise ship, but 28mph in relation to a nearby pier. (The ship and the pier are different reference points)
• Most times speed is measured using the Earth's surface as a reference point.

  

  The person's speed relative to the boat is 8mph, but relative to
  the pier it is 28mph (20 + 8).

  
  
• It is important to distinguish between average speed and instantaneous speed.
• An object's average speed is the total distance it travels within a certain time divided by this total elapsed time.
• A 1,500-mile flight that last 3 hours' average speed is 500mph (1,500-miles/3 hours = total distance/total elapsed time). This does not mean the plane was always traveling at a steady speed of 500mph.
• A runner that finished the 100-meter dash in 10 seconds' average speed is 10m/s, but he was not necessarily always running at this speed.
• Instantaneous speed is an object's speed in an instant in time; it can't be calculated like speed because an "instant" implies that 0 time passes, but to get an estimate we can calculate it using a very short time.
• A car's speedometer reads instantaneous speed, when it says 50mph it's saying that if you travel at the speed you're traveling in that instant for an hour, you'll cover 50 miles.
• We can use this pyramid as a trick to remember the speed, distance and time formulas.  If we cover what we're trying to find, we can get the formula to find it.
  
• To measure the speed of a segment of something that has already moved, we can take the final values (the ones we want to measure) minus the beginning values.  This is using the changes in distance and time to calculate instantaneous or average speed; speed would equal change in distance over change in time.
• The symbol Δ is the capital greek letter delta; it is used to represent a change in a physical quantity.
• When speed is constant, or the object travels at the same speed (the average speed would be the same as the instantaneous speed always), the relationship between the distance traveled and the time that has passed can be expressed as d = st (distance = speed x time).
• This is an example of a proportionality; d is proportional to t (abbreviated d ∝ t) because if we double the time, then the distance will be doubled as well.  Speed (v or s) is called the constant of proportionality; if it is constant because it will always be the same.
• The speed of light in empty space (c) is the universe's absolute speed limit; nothing has been observed traveling faster than c.
• Direction is an important aspect of motion because its change can produce effects that are equivalent to changing the speed; velocity is speed in a particular direction, it uses the same units as speed.
• Velocity changes whenever speed or direction changes; it can change without the speed changing.  If a car is going 15m/s north, and it curves and starts heading 15m/s east, its velocity changed but its speed didn't.
• With a speedometer (speed) and a compass (direction) we can calculate velocity.
• Velocity can be negative regarding another if it is going in the opposite direction (vector addition or subtraction); when a velocity is negative the negative symbol implies opposite direction, the speed does not become negative.  Speed can never be negative.
• If an airplane is said to be heading 200 miles due north; the displacement of the airplane is given.  Displacement is distance in a direction.
• Physical quantities can be classified as scalars or vectors.

• Scalars are quantities that are just made up of a magnitude and a unit; like speed, time, mass, and volume
• Vectors are quantities that include magnitude, a unit, and direction; they are represented by a proportional arrow in drawings.  Velocity, displacement, and momentum are vectors.
• Vector addition is the process through which we obtain the resultant or net velocity of an object.
• Two vectors are added by representing them as arrows and then positioning one arrow so its tip is at the tail of the other.  A new arrow drawn from the tip of the second is the arrow representing the resultant vector (sum of the two vectors).
  
• When the vectors are due the same direction (a) they're added, when they're due opposite directions (b) we subtract to obtain the resultant velocity.
• When two vectors are not along the same line we can't simply add or subtract their magnitudes.  We must draw the two arrows (head to tail) proportionally, to then draw and measure a resultant.  The resultant's direction is a combination of the two given; in the example below the bird is heading north and the wind is heading east, so the resultant velocity's direction would be northeast.

  

  The resultant velocity (10m/s NE) would be the bird's velocity relative to the ground.

• The Pythagorean theorem can also be used to calculate the magnitude of the resultant vector because vectors always form right triangles, and for any right triangle c² = a² + b².  Here, c stands for the resultant (hypotenuse, or longest side) and a and b are the other two legs of the triangle.
• Any vector can be seen as a resultant vector if we deconstruct it into two vectors.

1.3: Acceleration

• Acceleration is a vector quantity that defines the rate of change of velocity; it is calculated by dividing the change in velocity by the time elapsed (a = Δv/Δt)
  
• The relation between acceleration and velocity is the same as the one between velocity and displacement; acceleration indicates how rapidly velocity changes and velocity indicates how rapidly displacement changes.
• When something slows down (decreased speed) it is accelerating negatively (decelerating), the minus sign means the acceleration and the velocity (which is positive) are in opposite directions.
• A freefalling object is constantly accelerating downward at 9.8m/s² due to the force of gravity (g) only.
• Acceleration can also be determined by placing the two velocity proportional arrows, one with the beginning velocity (v₁), and another with the final velocity (v₂).  We can draw a third arrow (Δv) from the tip of the first one to the tip of the second one and then divide that quantity by the time elapsed between the two velocities to obtain acceleration.
  
• Centripetal acceleration is the acceleration of an object moving in a circular path; it's always perpendicular to the object's velocity.
• The magnitude of centripetal acceleration depends on speed (v) and radius (r) of the curve; a larger radius means a slower change in velocity (a = v² /r).
• Here, a ∝ v² and a ∝ 1/r (inversely proportional).  This means that when the speed is doubled, acceleration quadruples; and when the radius doubles, acceleration is halved.
• When we are in a bus and it curves and we move to that side, we are experiencing centripetal acceleration.
• Motion can be graphed by making a time vs distance (speed) graph.
• The rise of a graph goes vertically (y-axis value), the run goes horizontally (x-axis value); a graph's slope = rise/run.  The slope of a time vs distance graph would be speed.
  

  

  Remember: In a graph, the horizontal axis is the x-axis and
  the vertical axis is the y-axis.

Key Terms

1. physics - the study of the fundamental structures and interactions in the physical universe to better understand the universe and the things in it; seeks to discover the way in which things interact
2. mechanics - a primary branch of physics that studies motion and its causes
3. kinematics - how motion is described using the concepts of speed, velocity, and acceleration
4. distance - represents a measure of space in one direction; the MS unit is the meter
5. area - refers to the size of a surface: the number of squares (1 inch by 1 inch, for example) that would have to be added to cover it; the result is in units squared (^2)
   
6. volume - the number of cubes (1 cm per side, for example) needed to fill the shape it occupies; the result is in units cubed (^3)
   
7. time - periodical phenomena; process that repeats over and over at a regular rate
8. second - the universal unit of time, established using Earth's rotation
9. clock - measures time by using a process that repeats
10. period (T) - the time for one cycle of a process that repeats, abbreviated T; it's a measure of time, its units are seconds, minutes, etc.
11. pendulum - consists of a weight tied to the end of a string that swings back and forth
12. mean solar day - the average interval between successive crossings of your local meridian by the Sun
13. ephemeris second - based on Earth's motion around the Sun; was adopted in the late 1950s in sought of a more uniform time cycle than the Earth-Sun system
14. atomic second - based on using oscillations of light waves given off by isolated cesium atoms; established in 1967
15. Coordinated Universal Time (UTC) - introduced by the French Bureau International de l'Heure, the world's official timekeepers, in the early 1970s; the duration of the second is dictated by atomic time but is required to remain within 0.9 seconds of mean solar time
16. Global Positioning System (GPS) - system consisting in an array of 31 active satellites that circulate Earth every 12 hours; it was originally developed for the military but branches out into civilian use today
17. frequency (f) - the number of cycles that occur per time, abbreviated f; its standard unit is hertz (Hz)
18. hertz - the standard unit of frequency; equals 1 cycle per second (1/s)
19. mass - the measure of how much matter an object contains; the MS unit is the gram
20. inertia - resistance to change in speed (mass)
21. weight - vector of the force of gravity on mass
22. speed - rate of movement
23. reference point - point from where relative speed is measured
24. average speed - the total distance an object travels divided by the time it took to travel that distance
25. instantaneous speed - the speed of an object in an instant in time
26. speedometer - is found in cars and other vehicles; reads instantaneous speed
27. delta (Δ) - capital greek letter used to represent a change in a physical quantity; Δ is read as "change in"
28. proportionality (∝) - two physical quantities are proportional in a formula when if one is doubled, the other one doubles top; in d = st, d ∝ t (∝ is read "is proportional to")
29. direction - towards where motion goes; an important aspect of motion
30. velocity - speed in a particular direction, directed motion; uses the same units and formulas as speed
31. compass - a tool that gives us direction of motion
32. magnitude - numerical measurement in a physical quantity
33. scalar - physical quantity made up of magnitude and a unit
34. vector - physical quantity made up of magnitude, a unit, and direction
35. displacement - vector quantity that indicates distance in a specific direction
36. vector addition - the process through which we obtain the resultant or net velocity of an object by adding motion vectors
37. resultant vector - the result of a vector addition, the sum of the vectors
38. component vector - each factor of a resultant vector
39. Pythagorean theorem - used to calculate resultant vectors; states that for any right triangle c² = a² + b², c being the hypotenuse (longest side) and a and b being the other two legs
40. acceleration - rate of change of velocity (a = Δv/Δt)
41. deceleration - term used in everyday speech to indicate a decrease in speed; is encompassed in acceleration
42. freefall - condition in which an object is constantly accelerating downward and only the force of gravity is acting on it (ignoring forces like air resistance); a freefalling object falls at 9.8m/s²
43. centripetal acceleration - the acceleration of an object moving in a circular path; it is always perpendicular to the object's velocity
44. graph - concise and visual representation of data
45. Metric System (MS) - measure system used in science and everywhere except in the United States

Common Abbreviations and Formulas

Common abbreviations; there is also MS = Metric System.

Metric prefixes

Some of the common formulas. (f = 1/T*)

References

Ostdiek, Vern J., and Donald J. Bord. Inquiry into Physics. Pacific Grove, CA: Brooks/Cole, 2000. WebAssign. Web. 10 Oct. 2016.

Notes and additional information are integrated into the lesson summaries, but not all material is included.  Conversion factors, amongst other material, is not included in the review.