4 Linear Motion 4.1 Motion Is Relative
4 Linear Motion4 Linear Motion4.1 Motion Is RelativeYou can describe themotion of an object by itsposition, speed, direction,and acceleration.4 Linear MotionAn object is moving if its positionrelative to a fixed point is changing.4 Linear Motion4.1 Motion Is Relative4.1 Motion Is RelativeEven things that appear to be at rest move.When we describe the motion of one object withrespect to another, we say that the object is movingrelative to the other object. A book that is at rest, relative to the table it lieson, is moving at about 30 kilometers per secondrelative to the sun. The book moves even faster relative to thecenter of our galaxy.The racing cars in the Indy 500 move relative to the track.4 Linear Motion4 Linear Motion4.1 Motion Is Relative4.1 Motion Is RelativeWhen we discuss the motion of something, wedescribe its motion relative to something else. The space shuttle moves at 8 kilometers persecond relative to Earth below. A racing car in the Indy 500 reaches a speed of300 kilometers per hour relative to the track. Unless stated otherwise, the speeds of things inour environment are measured relative to thesurface of Earth.Although you may be at rest relative to Earth’s surface,you’re moving about 100,000 km/h relative to the sun.1
4 Linear Motion4 Linear Motion4.1 Motion Is Relative4.1 Motion Is Relativethink!think!A hungry mosquito sees you resting in a hammock in a 3meters-per-second breeze. How fast and in what directionshould the mosquito fly in order to hover above you for lunch?A hungry mosquito sees you resting in a hammock in a 3meters-per-second breeze. How fast and in what directionshould the mosquito fly in order to hover above you for lunch?Answer: The mosquito should fly toward you into the breeze.When above you it should fly at 3 meters per second in orderto hover at rest above you.4 Linear Motion4.1 Motion Is RelativeHow can you tell if an object is moving?4 Linear Motion4 Linear Motion4.2 SpeedYou can calculate the speed of anobject by dividing the distancecovered by time.4 Linear Motion4.2 Speed4.2 SpeedBefore the time of Galileo, people described moving thingsas simply “slow” or “fast.” Such descriptions were vague.Galileo is credited as being the first to measure speed byconsidering the distance covered and the time it takes.Speed is how fast an object is moving.Any combination of units for distance and time that areuseful and convenient are legitimate for describing speed: miles per hour (mi/h) kilometers per hour (km/h) centimeters per day light-years per century2
4 Linear Motion4 Linear Motion4.2 Speed4.2 SpeedA cheetah is the fastest land animal over distances lessthan 500 meters and can achieve peak speeds of 100 km/h.We will primarily use the unit meters per second (m/s)for speed.If a cheetah covers 50 meters in a time of 2 seconds, itsspeed is 25 m/s.4 Linear Motion4.2 Speed4 Linear Motion4.2 SpeedInstantaneous SpeedA car does not always move at the same speed.You can tell the speed of the car at any instant bylooking at the car’s speedometer.The speed at any instant is called theinstantaneous speed.4 Linear Motion4 Linear Motion4.2 Speed4.2 SpeedThe speedometer gives readings ofinstantaneous speed in both mi/h and km/h.Average SpeedIn a trip by car, the car will certainly not travel atthe same speed all during the trip.The driver cares about the average speed for thetrip as a whole.The average speed is the total distance covereddivided by the time.3
4 Linear Motion4 Linear Motion4.2 Speed4.2 SpeedAverage speed can be calculated easily:The average speed is often quite different from theinstantaneous speed.Whether we talk about average speed or instantaneousspeed, we are talking about the rates at which distanceis traveled.For example, a distance of 240 kilometers during a timeof 4 hours is an average speed of 60 km/h:4 Linear Motion4 Linear Motion4.2 Speed4.2 SpeedIf we know average speed and travel time, the distancetraveled is easy to find.think!total distance covered average speed travel timeIf a cheetah can maintain a constant speed of 25 m/s, it willcover 25 meters every second. At this rate, how far will ittravel in 10 seconds? In 1 minute?For example, if your average speed is 80 kilometers perhour on a 4-hour trip, then you cover a total distance of320 kilometers.4 Linear Motion4 Linear Motion4.2 Speed4.2 Speedthink!think!The speedometer in every car also has anodometer that records the distance traveled. If theodometer reads zero at the beginning of a trip and35 km a half hour later, what is the average speed?If a cheetah can maintain a constant speed of 25 m/s, it willcover 25 meters every second. At this rate, how far will ittravel in 10 seconds? In 1 minute?Answer: In 10 s the cheetah will cover 250 m, and in 1 min(or 60 s) it will cover 1500 m.4
4 Linear Motion4.2 Speedthink!The speedometer in every car also has anodometer that records the distance traveled. If theodometer reads zero at the beginning of a trip and35 km a half hour later, what is the average speed?4 Linear Motion4.2 SpeedHow can you calculate speed?Answer:4 Linear Motion4.3 VelocitySpeed is a description of how fast anobject moves; velocity is how fastand in what direction it moves.4 Linear Motion4 Linear Motion4.3 VelocityIn physics, velocity is speed in a given direction. When we say a car travels at 60 km/h, we arespecifying its speed. When we say a car moves at 60 km/h to thenorth, we are specifying its velocity.4 Linear Motion4.3 Velocity4.3 VelocityA quantity such as velocity that specifies directionas well as magnitude is called a vector quantity. Speed is a scalar quantity. Velocity, like force, is a vector quantity.Constant VelocityConstant speed means steady speed. Somethingwith constant speed doesn’t speed up or slowdown.Constant velocity means both constant speed andconstant direction.Constant direction is a straight line, so constantvelocity means motion in a straight line at constantspeed.5
4 Linear Motion4 Linear Motion4.3 Velocity4.3 VelocityChanging VelocityThe car on the circular track may have a constantspeed but not a constant velocity, because itsdirection of motion is changing every instant.If either the speed or the direction (or both) ischanging, then the velocity is changing. Constant speed and constant velocity are notthe same. A body may move at constant speed along acurved path but it does not move withconstant velocity, because its direction ischanging every instant.4 Linear Motion4 Linear Motion4.3 Velocity4.3 Velocitythink!think!The speedometer of a car moving northward reads 60 km/h.It passes another car that travels southward at 60 km/h. Doboth cars have the same speed? Do they have the samevelocity?The speedometer of a car moving northward reads 60 km/h.It passes another car that travels southward at 60 km/h. Doboth cars have the same speed? Do they have the samevelocity?Answer: Both cars have the same speed, but they haveopposite velocities because they are moving in oppositedirections.4 Linear Motion4.3 VelocityHow is velocity different from speed?4 Linear Motion4.4 AccelerationYou can calculate the acceleration ofan object by dividing the change inits velocity by time.6
4 Linear Motion4 Linear Motion4.4 Acceleration4.4 AccelerationWe can change the state of motion of an object bychanging its speed, its direction of motion, or both.Acceleration is the rate at which the velocity is changing.In physics, the term acceleration applies to decreases aswell as increases in speed.The brakes of a car can produce large retardingaccelerations, that is, they can produce a large decreaseper second in the speed. This is often called deceleration.4 Linear Motion4 Linear Motion4.4 Acceleration4.4 AccelerationA car is accelerating whenever there is a change in its stateof motion.A car is accelerating whenever there is a change in its stateof motion.4 Linear Motion4 Linear Motion4.4 Acceleration4.4 AccelerationA car is accelerating whenever there is a change in its stateof motion.Change in DirectionAcceleration also applies to changes in direction. It is important to distinguish between speedand velocity. Acceleration is defined as the rate of changein velocity, rather than speed. Acceleration, like velocity, is a vector quantitybecause it is directional.7
4 Linear Motion4 Linear Motion4.4 Acceleration4.4 AccelerationAccelerate in the direction of velocity–speed upAccelerate in the direction of velocity–speed upAccelerate against velocity–slow down4 Linear Motion4 Linear Motion4.4 Acceleration4.4 AccelerationAccelerate in the direction of velocity–speed upAccelerate against velocity–slow downAccelerate at an angle to velocity–change directionChange in Speed4 Linear MotionWhen straight-line motion is considered, it is common to usespeed and velocity interchangeably.When the direction is not changing, acceleration may beexpressed as the rate at which speed changes.4 Linear Motion4.4 Acceleration4.4 AccelerationSpeed and velocity are measured in units of distance pertime. Acceleration is the change in velocity (or speed) pertime interval. Acceleration units are speed per time. Changing speed, without changing direction, from 0km/h to 10 km/h in 1 second, acceleration along astraight line isThe acceleration is 10 km/h s, which is read as“10 kilometers per hour-second.”Note that a unit for time appears twice: once for the unit ofspeed and again for the interval of time in which the speed ischanging.8
4 Linear Motion4 Linear Motion4.4 Acceleration4.4 Accelerationthink!think!Suppose a car moving in a straight line steadily increasesits speed each second, first from 35 to 40 km/h, then from40 to 45 km/h, then from 45 to 50 km/h. What is itsacceleration?Suppose a car moving in a straight line steadily increasesits speed each second, first from 35 to 40 km/h, then from40 to 45 km/h, then from 45 to 50 km/h. What is itsacceleration?Answer: The speed increases by 5 km/h during each 1-sinterval in a straight line. The acceleration is therefore5 km/h s during each interval.4 Linear Motion4 Linear Motion4.4 Acceleration4.4 Accelerationthink!think!In 5 seconds a car moving in a straight line increases itsspeed from 50 km/h to 65 km/h, while a truck goes from restto 15 km/h in a straight line. Which undergoes greateracceleration? What is the acceleration of each vehicle?In 5 seconds a car moving in a straight line increases itsspeed from 50 km/h to 65 km/h, while a truck goes from restto 15 km/h in a straight line. Which undergoes greateracceleration? What is the acceleration of each vehicle?Answer: The car and truck both increase their speed by15 km/h during the same time interval, so their accelerationis the same.4 Linear Motion4.4 AccelerationHow do you calculate acceleration?4 Linear Motion4.5 Free Fall: How FastThe acceleration of an object in freefall is about 10 meters per secondsquared (10 m/s2).9
4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How FastFalling ObjectsDuring each second of fall the instantaneous speed of theobject increases by an additional 10 meters per second.This gain in speed per second is the acceleration.Imagine there is no air resistance andthat gravity is the only thing affecting afalling object. An object moving under theinfluence of the gravitational forceonly is said to be in free fall. The elapsed time is the time thathas elapsed, or passed, since thebeginning of any motion, in thiscase the fall.4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How FastWhen the change in speed is in m/s and the time interval is ins, the acceleration is in m/s2, which is read as “meters persecond squared.”The unit of time, the second, occurs twice—once for the unitof speed and again for the time interval during which thespeed changes.For free fall, it is customary to use the letter g to represent theacceleration because the acceleration is due to gravity.Although g varies slightly in different parts of the world, itsaverage value is nearly 10 m/s 2.Where accuracy is important, the value of 9.8 m/s 2 should beused for the acceleration during free fall.4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How FastThe instantaneous speed of an object falling from rest isequal to the acceleration multiplied by the elapsed time.v gtThe letter v represents both speed and velocity. When theacceleration g 10 m/s2 is multiplied by the elapsed time inseconds, the result is the instantaneous speed in meters persecond.If a falling rock weresomehow equipped with aspeedometer, in eachsucceeding second of fall itsreading would increase bythe same amount, 10 m/s.10
4 Linear Motion4.5 Free Fall: How Fast4 Linear Motion4.5 Free Fall: How FastThe average speed of any object moving in a straight linewith constant acceleration is the average of the initial speedand the final speed.The average speed of a freely falling object in its first secondof fall is the sum of the initial speed of zero and the finalspeed of 10 m/s, divided by 2, or 5 m/s.4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How FastRising ObjectsDuring the upward part of this motion, the object slows fromits initial upward velocity to zero velocity.The object is accelerating because its velocity is changing.How much does its speed decrease each second?Now consider an object thrown straight up: It moves upward for a while. At the highest point, when the object is changing itsdirection from upward to downward, its instantaneousspeed is zero. It then falls downward as if it had been dropped from restat that height.4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How FastThe speed decreases at the same rate it increases whenmoving downward—at 10 meters per second each second. The instantaneous speed at points of equal elevationin the path is the same whether the object is movingupward or downward. The velocities are different because they are inopposite directions. During each second, the speed or the velocitychanges by 10 m/s downward.The change in speed eachsecond is the samewhether the ball is goingupward or downward.11
4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How Fastthink!think!During the span of the second time interval in Table 4.2,the object begins at 10 m/s and ends at 20 m/s. What isthe average speed of the object during this 1-secondinterval? What is its acceleration?During the span of the second time interval in Table 4.2,the object begins at 10 m/s and ends at 20 m/s. What isthe average speed of the object during this 1-secondinterval? What is its acceleration?Answer: The average speed is 15 m/s. The accelerationis 10 m/s2.4 Linear Motion4 Linear Motion4.5 Free Fall: How Fast4.5 Free Fall: How Fastthink!think!What would the speedometer reading on the falling rockbe 4.5 seconds after it drops from rest?How about 8 seconds after it is dropped?What would the speedometer reading on the falling rockbe 4.5 seconds after it drops from rest?How about 8 seconds after it is dropped?Answer: The speedometer readings would be 45 m/s and80 m/s, respectively.4 Linear Motion4.5 Free Fall: How FastWhat is the acceleration of an object infree fall?4 Linear Motion4.6 Free Fall: How FarFor each second of free fall, an objectfalls a greater distance than it did inthe previous second.12
4 Linear Motion4 Linear Motion4.6 Free Fall: How Far4.6 Free Fall: How FarHow far does an object in free fall travel in the first second? At the end of the first second, the falling object has aninstantaneous speed of 10 m/s. The initial speed is 0 m/s. The average speed is 5 m/s. During the first second, the object has an averagespeed of 5 m/s, so it falls a distance of 5 m.Pretend that a falling rockis somehow equipped withan odometer. Thereadings of distance fallenincrease with time.4 Linear Motion4 Linear Motion4.6 Free Fall: How Far4.6 Free Fall: How FarAt the end of one second, the rock has fallen 5 meters.At the end of 2 seconds, it has dropped a total distanceof 20 meters.At the end of 3 seconds, it has dropped 45 metersaltogether.These distances form a mathematical pattern: at theend of time t, the object starting from rest falls adistance d.4 Linear Motion4.6 Free Fall: How Far4 Linear Motion4.6 Free Fall: How FarWe used freely falling objects to describe therelationship between distance traveled, acceleration,and velocity acquired.The same principles apply to any accelerating object.Whenever an object’s initial speed is zero and theacceleration a is constant, velocity and distancetraveled are:13
4 Linear Motion4 Linear Motion4.6 Free Fall: How Far4.6 Free Fall: How Farthink!think!An apple drops from a tree and hits the ground in onesecond. What is its speed upon striking the ground? Whatis its average speed during the one second? How highabove ground was the apple when it first dropped?An apple drops from a tree and hits the ground in onesecond. What is its speed upon striking the ground? Whatis its average speed during the one second? How highabove ground was the apple when it first dropped?Answer: The speed when it strikes the ground is 10 m/s.The average speed was 5 m/s and the apple droppedfrom a height of 5 meters.4 Linear Motion4.6 Free Fall: How FarFor a falling object, how does thedistance per second change?4 Linear Motion4 Linear Motion4.7 Graphs of MotionOn a speed-versus-time graph theslope represents speed per time,or acceleration.4 Linear Motion4.7 Graphs of Motion4.7 Graphs of MotionEquations and tables are not the only way to describerelationships such as velocity and acceleration.Graphs can visually describe relationships.Speed-Versus-TimeOn a speed-versus-time graph, the speed v of a freely fallingobject can be plotted on the vertical axis and time t on thehorizontal axis.14
4 Linear Motion4 Linear Motion4.7 Graphs of Motion4.7 Graphs of Motion This particular linearity is called a direct proportion,and we say that time and speed are directly proportionalto each other. The “curve” that best fits the points forms a straight line.For every increase of 1 s, there is the same 10 m/sincrease in speed.Mathematicians call this linearity.Since the object is dropped from rest, the line starts atthe origin, where both v and t are zero.If we double t, we double v; if we triple t, we triple v; andso on.4 Linear Motion4 Linear Motion4.7 Graphs of Motion4.7 Graphs of MotionThe curve is a straight line, so its slope is constant.Slope is the vertical change divided by the horizontalchange for any part of the line.For 10 m/s of vertical change there is a horizontalchange of 1 s.The slope is 10 m/s divided by 1 s, or 10 m/s 2.The straight line shows the acceleration is constant.If the acceleration were greater, the slope of the graphwould be steeper.4 Linear Motion4 Linear Motion4.7 Graphs of Motion4.7 Graphs of MotionDistance-Versus-TimeThis distance-versus-time graph is parabolic.When the distance d traveled by a freely falling object isplotted on the vertical axis and time t on the horizontal axis,the result is a curved line.15
4 Linear Motion4 Linear Motion4.7 Graphs of Motion4.7 Graphs of MotionThe relationship between distance and time is nonlinear.The relationship is quadratic and the curve is parabolic—when we double t, we do not double d; we quadruple it.Distance depends on time squared!A curved line also has a slope—different at different points.The slope of a curve changes from one point to the next.The slope of the curve on a distance-versus-time graph isspeed, the rate at which distance is covered per unit of time.The slope steepens (becomes greater) as time passes, whichshows that speed increases as time passes.4 Linear Motion4.7 Graphs of MotionWhat does a slope of a speed-versustime graph represent?4 Linear Motion4 Linear Motion4.8 Air Resistance and Falling ObjectsAir resistance noticeably slows the motion ofthings with large surface areas like fallingfeathers or pieces of paper. But air resistanceless noticeably affects the motion of morecompact objects like stones and baseballs.4 Linear Motion4.8 Air Resistance and Falling Objects4.8 Air Resistance and Falling ObjectsDrop a feather and a coin and the coin reaches the floor farahead of the feather.Air resistance is responsible for these different accelerations.In a vacuum, the feather and coin fall side by side with thesame acceleration, g.A feather and a coin accelerate equallywhen there is no air around them.16
4 Linear Motion4.8 Air Resistance and Falling Objects4 Linear Motion4.8 Air Resistance and Falling ObjectsIn many cases the effect of air resistance is small enough tobe neglected.With negligible air resistance, falling objects can beconsidered to be falling freely.How does air resistance affectfalling objects?4 Linear Motion4.9 How Fast, How Far, How Quickly HowFast ChangesAcceleration is the rate at which velocityitself changes.4 Linear Motion4.9 How Fast, How Far, How Quickly HowFast ChangesOne of the most confusing concepts encountered in this bookis acceleration, or “how quickly does speed or velocitychange.”What makes acceleration so complex is that it is a rate of arate. It is often confused with velocity, which is itself a rate(the rate at which distance is covered).Acceleration is not velocity, nor is it even a change in velocity.4 Linear Motion4.9 How Fast, How Far, How Quickly HowFast ChangesDon’t mix up “how fast” with “how far.” How fast something freely falls from rest after a certainelapsed time is speed or velocity. The appropriateequation is v gt. How far that object has fallen is distance. Theappropriate equation is d 1/2gt2.4 Linear Motion4.9 How Fast, How Far, How Quickly HowFast ChangesWhat is the relationship betweenvelocity and acceleration?17
4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions1.1.Jake walks east through a passenger car on a train that moves 10m/s in the same direction. Jake’s speed relative to the car is 2 m/s.Jake’s speed relative to an observer at rest outside the train isa. 2 m/s.b. 5 m/s.c. 8 m/s.d. 12 m/s.Jake walks east through a passenger car on a train that moves 10m/s in the same direction. Jake’s speed relative to the car is 2 m/s.Jake’s speed relative to an observer at rest outside the train isa. 2 m/s.b. 5 m/s.c. 8 m/s.d. 12 m/s.Answer: D4 Linear MotionAssessment Questions2.A gazelle travels 2 km in a half hour. The gazelle’s average speed isa. 1/2 km/h.b. 1 km/h.c. 2 km/h.d. 4 km/h.4 Linear MotionAssessment Questions2.A gazelle travels 2 km in a half hour. The gazelle’s average speed isa. 1/2 km/h.b. 1 km/h.c. 2 km/h.d. 4 km/h.Answer: D4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions3.3.Constant speed in a constant direction isa. constant velocity.b. constant acceleration.c. instantaneous speed.d. average velocity.Constant speed in a constant direction isa. constant velocity.b. constant acceleration.c. instantaneous speed.d. average velocity.Answer: A18
4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions4.4.A vehicle undergoes acceleration when ita. gains speed.b. decreases speed.c. changes direction.d. all of the aboveA vehicle undergoes acceleration when ita. gains speed.b. decreases speed.c. changes direction.d. all of the aboveAnswer: D4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions5.5.If a falling object gains 10 m/s each second itfalls, its acceleration can be expressed asa. 10 m/s/s.b. 10 m/s2.c. v gt.d. both A and B.If a falling object gains 10 m/s each second itfalls, its acceleration can be expressed asa. 10 m/s/s.b. 10 m/s2.c. v gt.d. both A and B.Answer: D4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions6.6.A rock falls 180 m from a cliff into the ocean. How long is it in freefall?a. 6 sb. 10 sc. 18 sd. 180 sA rock falls 180 m from a cliff into the ocean. How long is it in freefall?a. 6 sb. 10 sc. 18 sd. 180 sAnswer: A19
4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions7.7.The slope of a speed-versus-time graph representsa. distance traveled.b. velocity.c. acceleration.d. air resistance.The slope of a speed-versus-time graph representsa. distance traveled.b. velocity.c. acceleration.d. air resistance.Answer: C4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions8.8.In a vacuum tube, a feather is seen to fall as fast as a coin. This isbecausea. gravity doesn’t act in a vacuum.b. air resistance doesn’t act in a vacuum.c. greater air resistance acts on the coin.d. gravity is greater in a vacuum.In a vacuum tube, a feather is seen to fall as fast as a coin. This isbecausea. gravity doesn’t act in a vacuum.b. air resistance doesn’t act in a vacuum.c. greater air resistance acts on the coin.d. gravity is greater in a vacuum.Answer: B4 Linear Motion4 Linear MotionAssessment QuestionsAssessment Questions9.9.Speed and acceleration are actuallya. one and the same concept, but expressed differently.b. rates of one another.c. entirely different concepts.d. expressions of distance traveled.Speed and acceleration are actuallya. one and the same concept, but expressed differently.b. rates of one another.c. entirely different concepts.d. expressions of distance traveled.Answer: C20
relative to the other object. A book that is at rest, relative to the table it lies on, is moving at about 30 kilometers per second relative to the sun. The book moves even faster relative to the center of our galaxy. 4.1 Motion Is Relative 4 Linear Motion The racing cars in the Indy 500 move relative
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4 Linear Motion We will primarily use the unit meters per second (m/s) for speed. If a cheetah covers 50 meters in a time of 2 seconds, its speed is 25 m/s. 4.2 Speed 4 Linear Motion 4.2 Speed 4 Linear Motion Instantaneous Speed A car does not always move at the same speed. You can tell the speed of the car at any instant by
HELIX LINEAR IS A GLOBAL LEADER IN LINEAR MOTION TECHNOLOGIES. For nearly 50 years the company has helped its customers engineer their own sucess in a wide range of markets. Helix Linear leads with its innovative design, engineering, and manufacturing of precision linear motion and power transmission systems. Helix Linear focuses on engineering and
Lesson 14: Simple harmonic motion, Waves (Sections 10.6-11.9) Lesson 14, page 1 Circular Motion and Simple Harmonic Motion The projection of uniform circular motion along any axis (the x-axis here) is the same as simple harmonic motion. We use our understanding of uniform circular motion to arrive at the equations of simple harmonic motion.
Simple Harmonic Motion The motion of a vibrating mass-spring system is an example of simple harmonic motion. Simple harmonic motion describes any periodic motion that is the result of a restoring force that is proportional to displacement. Because simple harmonic motion involves a restoring force, every simple harmonic motion is a back-
Motion Capture, Motion Edition - lionel.reveret@inria.fr 38 Motion capture, Motion edition References – "Motion Warping,“, Zoran Popovic, Andy Witkin in Com puter Graphics (SIGGRAPH) 1995. – Michael Gleicher. “Retargetting Motion to New Chara cters”, Proceedings of SIGGRAPH 98. In Computer Graphics Annual Conferance Series. 1998.
Motion-Based Motion Deblurring Moshe Ben-Ezra and Shree K. Nayar,Member, IEEE Abstract—Motion blur due to camera motion can significantly degrade the quality of an image. Since the path of the camera motion can be arbitrary, deblurring of motion blurred images is a hard problem. Previ
the legal reasons each party included in their written motion or answer to motion briefs. The party making a motion to the court, or the "moving party," must serve a notice of motion on all other parties. The notice of motion is served with the motion, brief in support of motion,
