Kinematics Concepts
QuestionAnswerMotion is when an object changes itslocation, or position.QuestionIf an object is not moving, it stays at thesame place (position).AnswerKinematics: How do we describemotion in a way that everyone canunderstand, using numbers?What are the 2 big questions we wantto answer in physics about motion?Which quantities can we measure?What quantities can we calculate?Forces: How do we explain motion?What causes object to move the way theydo?Unit 2 - Kinematics ConceptsWhat is motion, to a physicist?
AnswerWhat are the 4 basic types of motion?1. Linear Motion – motion in astraight or curved path2. Circular Motion – motion in a circle3. Vibration Motion – motion of anobject that goes back-and-forth4. Rotational motion – spinning of anobject (e.g., Earth is spinning)QuestionWhat are examples of linear motion(in a straight line)?AnswerExamples of motion in a straight line: Bowling ball rolling in a straight line Car moving on a straight road Ball dropped from a cliff Can you think of your ownexamples?Unit 2 - Kinematics ConceptsQuestion
What is 1-dimensional motion(or “1D motion”)?QuestionWhat is 2-dimensional motion(or “2D motion”)?Answer1D motion is motion in a straight line.So, you need only 1 number(or 1 dimension) to locate the objecton a number line.Answer2D motion is when you need2 numbers (or 2 dimensions) to locatethe object (e.g., x and y coordinates).y(x,y)You need x and ycoordinates to labelthe position of the ballxUnit 2 - Kinematics ConceptsQuestion
QuestionAnswerYou can measure the base quantities distance (orlength) and time. Also, direction.Example: You use formulas to calculate(not measure):average speedaverage velocityQuestionsavg change in velocity vvavg acceleration aAnswerVariables withmagnitude only(scalars)Which variables describe motion?(scalars and vectors)ddistancettimesavgaveragespeedVariables that have bothmagnitude anddirection (vectors) x displacementv velocity, includingaverage, initial, andfinal velocitiesvavgvia accelerationvfUnit 2 - Kinematics ConceptsWhich variables can we measuredirectly to describe motion?All other variables related to motion must becalculated using a formula.
What is the difference between scalarand vector quantities?QuestionAnswerScalar is a variable that only has magnitude(number and unit), but no direction.Examples of scalar variables:distance d 2m, time t 3s,mass m 10kg, temperature T 200KVector is a variable that has both magnitude anddirection.Examples of vector variables:displacement x 20 km Southvelocity v -10m/s Northacceleration a 2 m/s2AnswerDraw a vector as an arrow, pointing in the correctdirection. Size of arrow represents magnitude(“how much”).Example: Velocity vector (units m/s)How do you draw vectors?2 m/sLabel themagnitude in themiddle of thearrow.Units show the kindof variable (e.g.,velocity is in m/s)Unit 2 - Kinematics ConceptsQuestion
List all vector quantities thatdescribe motion.AnswerVector quantities have both magnitude anddirection. Magnitude is the number units. Direction is N-S-W-E or “ ” or “-”. x Displacement m or mivInclude symbols and units.vavgaQuestionList all scalar motion thatdescribe motion.Include symbols and units.Velocity, including average, initial, and finalvelocity. Units or m/s or mi/h.vivfAcceleration in m/s2 or mi/h2AnswerScalar quantities have only magnitude, andno direction. Magnitude is the number units.For motion, the following are scalars:ddistance in m or mittime in s or minsavgaverage speed inm/s or mi/hUnit 2 - Kinematics ConceptsQuestion
QuestionAnswerA dot diagram shows where the objectis located at equal time intervals.What is a “dot” diagram?Numbers show the order of positionsQuestionAnswerParticle Model: You simplify moving objectsby assuming they are solid “dots.”What is theParticle Model?The Particle Model shows how differentobjects can have the same motion(e.g., diver and rock).RockDiverDot diagrams are useful when the shape andsize of an object do not affect motion.Unit 2 - Kinematics ConceptsEqual time passes between dots (e.g., 1s)
QuestionHow do you draw a dot diagram?Answer1. Draw a dot for each position at equal time intervals(e.g., 1s apart).2. Constant speed – equal spacing; Speeding up –increase spacing; Slow down - decrease spacing3. Arrows between dots show vectors of average velocityduring each time interval.0sMovingRightconstant speedspeed upMovingLeftQuestionWhen is it not correct to use theParticle Model?(i.e., assume that objects are “dots”)constant speedspeed upslow down0sAnswerWhen the motion you want to study isaffected by Size of object Shape of object How mass is spread out in objectEx: Can’t use a Particle Model to studyrotation. How objects rotate depends ontheir shape and how the mass is spread out.Unit 2 - Kinematics Conceptsslow down
AnswerDistance“d”Distance is the length of the path an objectmoves.Symbol: dUnits: any distance units (e.g., m, km, mi)Scalar: can only be positiveStartd 20 miQuestionEndAnswerTime Instant“t”Time instant lets you assign a number andunit to when an object is at a specificposition “x”.Symbol: tUnits: any time units (e.g., s, min, hr or h)Scalar: can only be positiveExample: If the time interval between the dotsis 1s, at t 3s the object is at x 2.5mUnit 2 - Kinematics ConceptsQuestion
Time Interval“ t”(pronounced “Delta t”)AnswerTime interval is how much time passesbetween two time instants.Symbol: tFormula: t t f tiUnits: any time units (e.g., s, min, hr or h)Scalar: can only be positive (clocks moveforward)Usually, the start time is 0s and t is just t –the time your clock reads at the end.QuestionAnswerTime instant t does not last – it’s a moment.“At this instant, the timer reads 11:00:01s.”What is the difference between “t”and “ t”?Time interval t is how much time haspassed.“The runner ran 10 mi during the timeinterval of 2 min.”“The time interval between the dots on thedot diagram is 1s.”Unit 2 - Kinematics ConceptsQuestion
AnswerPosition“x”Position how far an object is away from “0”on a coordinate system.Symbol: xUnits: any distance units (e.g., m, km, mi)Vector: can be on positive or negative sideof zero - sign means directionx -5 miQuestionx 4 miAnswerA coordinate system lets you assign anumber and unit to the position “x” of anobject.What is a coordinate system?Example: A number line is a 1-dimensionalcoordinate system.Without a coordinate system, you could notmeasure position – the key variable to turn motionideas into measurable numbers and units!Unit 2 - Kinematics ConceptsQuestion
QuestionAnswer (or “Delta”) tells you to subtract“final” – “initial” value of the variable after itQuestion x means “subtract two positions”called displacement x x f xi v means “subtract two velocities”called change in velocity v v f viAnswerdisplacement“ x”Displacement is the straight-line distancefrom start to finish during a time interval.Symbol: xFormula: x x f xixi is initial position, x f is final positionUnits: any distance units (e.g., m, km, mi)Vector: Positive or negative, sign meansdirectionxxifx (m)Unit 2 - Kinematics ConceptsWhat is ? t means “subtract two time instants” t t tficalled time interval
What is the difference betweendistance and displacement?AnswerDistance d is the total length of the path youtook to get from one place to another –doesn’t have to be straight.Displacement x is the straight-line distancefrom start to finish.xi xxfdQuestionCan displacement be larger than thedistance traveled?AnswerDisplacement x is the straight-line distancefrom start to finish.The shortest distance between two points isa straight line – the displacement.Displacement can be equal to the distance,but it can’t be larger because it is theshortest distance between positions.Unit 2 - Kinematics ConceptsQuestion
QuestionAnswerAverage speed is the average or constant distancethe object moves each unit of time.Scalar: can only be positiveSavg 40 mi/hrQuestionAnswerHow to calculate average speed,distance or time usingsavg d tThe formula for average speed is defined to find“how fast” objects move, on average.The formula connects 3 variables: d (distance), t(time interval), and Savg.dIf you know d and t, you can solvesavg tfor Savg. d savg tIf you know Savg and t, you cansolve for d.d t savgIf you know d and Savg, you can solvefor t.Unit 2 - Kinematics ConceptsAverage Speed Definition“Savg”dFormula: savg tdistanceUnits: anyunits (e.g., m/s, km/h)time
QuestionAnswerAverage velocity is the average or constantdistance the object moves each unit of time. xv avgSymbol: tUnits: anydistanceunits (e.g., m/s, km/h)timeVector: can be positive or negativeSavg 40 mi/hrAnswerQuestionHow to calculate average velocity,displacement, or time usingvavg x tThe formula for average velocity Vavg is defined describe“how fast” an object moves in a straight line from start tofinish.The formula connects 3 variables: x (displacement), t(time interval), and Vavg. Same formula, rearranged 3 waysusing algebra.vavg x tIf you know x and t, you cansolve for Vavg. x vavg tIf you know Vavg and t, you cansolve for x. x t vavgIf you know x and Vavg, you cansolve for t.Unit 2 - Kinematics ConceptsAverage Velocity Definition(or “Vavg”)
What is the difference betweenaverage speed and average velocity?AnswerAvg. Speed is the average distance traveledper unit time, calculated from scalars.Scalar - always positive.Avg. Velocity is the average displacementfrom start to finish per unit time.Vector – can be negative or positive.xivavgxfsavgQuestionCan average velocity be larger thanaverage speed?AnswerAverage Velocity depends on displacement,which is the straight-line distance fromstart to finish.The shortest distance between two points isa straight line – the displacement.Average Speed depends on distance, whichcan be longer than or equal todisplacement, but it can’t be shorter.Unit 2 - Kinematics ConceptsQuestion
QuestionWhat are the 3 controls in the car thataccelerate the car?AnswerIn physics, “acceleration” means speeding up,slowing down, and/or changing direction.This is different from the real-world definition ofjust speeding up!Brake – slows down the carSteering wheel – changes directionQuestionWhy is an object that moves in a circlealways accelerating?(even if its speed is constant)AnswerIn physics, “acceleration” means changing velocity- speeding up, slowing down, and/or changingdirection.An object moving in a circle is always changingdirection.Therefore, it is changing its velocity (whether it’smoving at constant speed, speeding up, orslowing down).Therefore, it is accelerating (acceleration is changein velocity).Unit 2 - Kinematics ConceptsGas pedal – speeds up the car
QuestionAnswerAverage acceleration is the change in velocity ofobject each unit of time.Units: any v v f vi ttspeedunits (e.g., m/s2, km/h2)timeVector: can be positive or negativeQuestionAnswerHow to calculate average velocity,displacement, or time usinga v f vitThe formula for average acceleration a is defined todescribe “how fast” an object changes its velocity.The formula connects 3 variables: v (change in velocity), t (time interval), and a. Same formula, rearranged 3ways using algebra.a v f vitv f vi att v f viaIf you know Vi, Vf, and t, you cansolve for a.If you know Vi, a, and t, you cansolve for Vf.If you know Vf, Vi, and a, you cansolve for t.Unit 2 - Kinematics ConceptsAverage Acceleration Definition(or “a”)aSymbol:
A car with and initial velocity is 20 m/shas an acceleration of 5 m/s2.What is the velocity of the car after 2 s?QuestionA car with and initial velocity of 20 m/sWest has an acceleration of 5 m/s2 East.What is the velocity of the car after 3 s?Answerv 20m/sv 25m/sv 30m/sv 35m/st 0st 1st 2st 3s5 m/s2At 2s, the car is moving at 30 m/s to the right.Explanation: Initial velocity and acceleration areboth positive (point to the right). Each next 1second, the car speed up 5 m/s.Answerv 0 v 5m/st 4 s t 3sv 10m/st 2sv 15m/st 1sv 20m/st 0s5 m/s2At 3s, the car is moving at 5 m/s West.Explanation: Initial velocity and acceleration are inopposite directions. Each next 1 second, the carslows down 5 m/s while traveling West.Unit 2 - Kinematics ConceptsQuestion
QuestionAnswerNo. Speeding up or slowing down depends on thedirection of both velocity and acceleration.(e.g., - 3 m/s2)aaSlowing down is when velocity and accelerationpoint in opposite directions.vvaQuestionaAnswerYes.Can Position, Displacement, Velocityand Acceleration bepositive or negative?Positive/Negative indicate direction.Position, Displacement, Velocity, andAcceleration are all vectors and havedirection.Unit 2 - Kinematics ConceptsDoes negative acceleration alwaysmean “slowing down”?Speeding up is when velocity and accelerationpoint in the same direction.vv
QuestionAnswerIf an object is speeding up,C) Its acceleration can be positive ornegative depending on the velocitydirection (or direction of motion).An object speeds up when both velocityand acceleration “work together” andpoint in the same direction.vavaQuestionAnswerA truck is moving to the left withincreasing speed. Which dot diagramshows this motion?B) The average velocity vectors point left, so thetruck is moving left.The spacing between dots increases duringequal time intervals. The truck travels moredistance during each next 1 second.Thus, the truck is speeding up.Unit 2 - Kinematics ConceptsA. Its acceleration is positive.B. Its acceleration is negative.C. Its acceleration can be positive ornegative depending on the directionof motion.
QuestionAnswerSpeed or velocityvavg x tsavg d tSpeed/Velocity have units of distance divided bytime.Example: “Object travels 10 m every 1 s.”QuestionAnswerAccelerationUnits come from equation for acceleration:m/s2mi/h2orare units of which quantity?a v f vitAcceleration has units of speed per second.Example: “a 5m/s2 means speed change in thepositive direction 5 m/s each 1 s.”Unit 2 - Kinematics Conceptsm/s or mi/hare units of which quantity?Units come from equations of avg. speed and avg.velocity:
Answerm or mi are units of which quantity?QuestionDistance or displacementAnswerYes.Can Position, Displacement, Velocityand Acceleration bepositive or negative?Positive/Negative indicates direction.Position, Displacement, Velocity, andAcceleration are all vectors and havedirection.Unit 2 - Kinematics ConceptsQuestion
Draw displacement vectors of themotion:Answer x f2 km1 km3 kmWEx (km)02xi3 Draw vectors correct length Label key position (not all positions) Label magnitudes above each vector(positive)QuestionDraw displacement vectors of themotion:Answer Draw vectorscorrect length Label keyposition (not x fall positions) Labelmagnitudesxinext to eachvector(positive)N (km)2.51 km1.52.5 kmSUnit 2 - Kinematics ConceptsQuestion
Find total distance and displacement:Answer x f2 km1 km3 kmWEx (km)02xi3 Add magnitudes of displacements.Distance: d (3 2 1) km 6 km Displacement is x x f xi 0 0 0kmQuestionDraw displacement vectors of themotion:Answer Distance:d (2.5 1)km 3.5 kmN (km)2.51 kmx f 1.52.5 km Displacement: x x f xi 1.5 0 1.5kmxiS xUnit 2 - Kinematics ConceptsQuestion
Calculate Total DisplacementFrank travels from a position of 25 m to-20 m. Then, Frank travels to a positionof 5 m.What is Frank’s total displacement?(Show all calculations and units.)QuestionDraw Total Displacement VectorFrank travels from a position of 25 m to-20 m. Then, Frank travels to a positionof 5 m.Draw Frank’s total displacement vector.Label the magnitude.AnswerDraw a diagram of Frank’s trip: x ?The initial position is x1 25 m, and the finalposition for the trip is x3 5 m. x x3 x1 5m 25m 20mFrank’s total displacement is 20 m to the left.20 m is the magnitude, left (“-”) is the direction.AnswerDraw a diagram of Frank’s trip:20 mDraw the total displacement arrow “start tofinish” - from the initial position x1 25 m tothe final position for the trip x3 5 m.Label the magnitude above the middle of thevector as 20 m (magnitude is always positive).Unit 2 - Kinematics ConceptsQuestion
Find Average SpeedMolly travels 10 mi North to themarket, and then 20 mi South to herworkout. The total trip takes 2h.What is Molly’s average speed for theentire trip?QuestionFind Time at Constant SpeedDrake travels 20 mi at a speed of 60mi/h.How long was Drake driving?AnswerAverage speed or Savg is a scalar – it doesnot depend on direction.savg d tTo find Savg, you need to know the totaldistance d and the total time interval t ofthe tripsavg d 10mi 20mi 30mimi 15 th2h2hAnswer“How long” means “find time”, or t. Theentire trip is at constant speed(no acceleration).Have:Need:Savg 60 mi/h t ?d 20 middUse:savg tSolve for time tsavgd20mimi t 0.3savg 60mi / hhUnit 2 - Kinematics ConceptsQuestion
Find AccelerationMolly starts at 10 m/s and acceleratesto 30 m/s in 2 s.What is Molly’s acceleration?Show all calculations and units.Answervi 10m / sv f 30m / st 2sa ? x ?Need a. Use no x equation. av f vi 30m / s 10m / s 20m / sm 10 22s2stsNote: Underline and label variables in the problems.QuestionAnswerFind Time During Accelerated MotionDrake start at rest and accelerates at6m/s2 to 30 m/s.“How long” means “find time”, or t.v f 30m / svi 0t 2sa 6m / s 2 x ?How long does it take Drake to reachhis final speed? av f vit tv f viaSolve for timev f vi 30m / st 5sa6m / s 2Unit 2 - Kinematics ConceptsQuestion
QuestionAnswerAlgebra with UnitsHow do you get “seconds from thefollowing expression?Divide the units just like you divide twofractions:QuestionDrawing Dot DiagramsA car speeds up from rest, traveling to theright. Then, the car continues at constantspeed. Finally, the car slows down to a stop.Draw a dot diagram of this situation. Includeaverage velocity and acceleration vectors.Multiply the top fraction by the inverse ofthe bottom fraction. Cancel units.AnswerThe car travels to the right: Speeding up – dot spacing increases Constant speed – equal dot spacing Slowing down – dot spacing decreasesaa 0Speeding upConstant speedaSlowing downUnit 2 - Kinematics Conceptsm/s sm / s2m/sm s2 sm / s2s m
QuestionAnswerFree fall is a model that simplifies “real fall”by ignoring (“neglecting”) air resistance.Free fall assumes that only the force ofgravity affect the motion of an object.In free fall, all object fall at the same rate –regardless of mass or weight.Example: feather and ball in vacuumchamberQuestionAnswerOn Earth, air resistance slows motion.However, free fall applies when:When does the free-fall model apply?(or When does the model fail?) Object has a large mass Object is compact (small surface area) Object “falls” for a short time anddistanceNote: “Falls” is in quotes because objectscould be going up or down.Unit 2 - Kinematics ConceptsWhat is Free Fall?
QuestionAnswer“g” is a symbol for the acceleration ofgravity in free fall.(assuming free fall)On Earth, g -10 m/s2 (in MCAS formulas)(9.81 is more accurate but we use 10 makecalculations easier).g is a vector and points toward the center ofthe Earth (down).QuestionAnswerWhat is “g”?“g” is a symbol for the acceleration ofgravity in free fall.“g” is the same as “a” (acceleration vector),but refers to a special type of acceleration.On Earth, g - 10 m/s2(9.81 is more accurate, but we use 10 makecalculations easier).Unit 2 - Kinematics ConceptsWhat is the acceleration of gravity “g”on Earth?
Do all objects in space (planets, stars,asteroids) have the same “g” at theirsurface?QuestionAnswerNo. The value of “g” depends on the mass of theobject. Objects with more mass accelerate freefall objects faster.AnswerNo.Does Free Fall applies only to objectfalling down?Free-Fall just means only gravity is affectingthe object’s motion (and no other forces).The object could
Kinematics Concepts Question . Question Answer . Answer . 1. Linear Motion – motion in a straight or curved path . 2. Circular Motion – motion in a circle . 3. Vibration Motion – motion of an object that goes back-and-forth . 4. Rotational
28.09.2016 Exercise 1a E1a Kinematics Modeling the ABB arm 04.10.2016 Kinematics 2 L3 Kinematics of Systems of Bodies; Jacobians 05.10.2016 Exercise 1b L3 Differential Kinematics and Jacobians of the ABB Arm 11.10.2016 Kinematics 3 L4 Kinematic Control Methods: Inve rse Differential Kinematics, Inverse
4-1C Solution We are to define and explain kinematics and fluid kinematics. Analysis Kinematics means the study of motion. Fluid kinematics is the study of how fluids flow and how to describe fluid motion. Fluid kinematics deals with describing the motion of fluids without considering (or even understanding) the forces and moments that cause .
The study of mechanics in the human body is referred to as biomechanics. Biomechanics . Kinematics Kinetics . U. Kinematics: Kinematics is the area of biomechanics that includes descriptions of motion without regard for the forces producing the motion. [It studies only the movements of the body.]
The 12th International Conference on Advanced Robotics – ICAR 2005 – July 2005, Seattle WA (a) (b) Fig. 4: Time histories and statistics of the kinematics and dynamics of the human arm during an arm reach to head level (action 2): (a) Time histories of the joint kinematics and dynamics (b) Statistical distribution of the joint kinematics and dynamics.
1-D Kinematics: Horizontal Motion We discussed in detail the graphical side of kinematics, but now let’s focus on the equations. The goal of kinematics is to mathematically describe the trajectory of an object over time. T
kinematics, and it is, in general, more difficult than the forward kinematics problem. In this chapter, we begin by formulating the general inverse kinematics problem. Following this, we describe the principle of kinematic decoupling and how it can be used
Physics 11 Ñ Kinematics 1 Physics 11 Ñ Kinematics 1.1 Ñ Graphing Motion Kinematics is the study of motion without reference to forces and masses. We will need to learn some definitions: A Scalar quantity is a measurement that has a magnitude only: mass, distance, speed, energy, timeÉ A ve
Kinematics Kinematics pertains to the motion of bodies in a ro-botic mechanism without regard to the forces/torques that cause the motion. Since robotic mechanisms are by their very essence designed for motion, kinematics is the most fundamental aspect of robot design, anal
