Kinematics is the study of objects in motion.
We study distance, displacement, speed, velocity, and acceleration.
A common way of analyzing the motion of objects in physics labs is to perform a ticker tape analysis.
A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time – say every 0.10 second.
As the object moves, it drags the tape through the “ticker”:
It leaves a trail of dots. The dots provides a history of the object’s motion, and therefore a representation of the object’s motion.
- “Ticker Tape Diagrams, The Physics Classroom”
Great! Wait… what the heck is “ticker tape”?!!!
Ticker tape was the earliest digital electronic communications medium, transmitting stock price information over telegraph lines, in use between around 1870 through 1970. It consisted of a paper strip that ran through a machine called a stock ticker, which printed abbreviated company names as alphabetic symbols followed by numeric stock transaction price and volume information. The term “ticker” came from the sound made by the machine as it printed.
Paper ticker tape became obsolete in the 1960s, as television and computers were increasingly used to transmit financial information. The concept of the stock ticker lives on, however, in the scrolling electronic tickers seen on brokerage walls and on financial television networks.
– Wikipedia, Ticker Tape, 91/16
What is a ticker-tape parade?
A ticker tape parade is a parade event held in a city, with large amounts of shredded paper (originally actual ticker tape, but now mostly confetti) to be thrown from nearby office buildings onto the parade route, creating a celebratory effect by the snowstorm-like flurry. The term originated in New York City after a spontaneous celebration held on October 28, 1886, during the dedication of the Statue of Liberty and is still most closely associated with New York City.
Scalars and vectors
Scalar – the type of number that you’re used to. A single number.
Scalars describe size/magnitude, like: speed, height, volume, age, temperature
Vectors – a number and a direction. Here are some examples:
velocity – 30 miles/hour, east
force – 100 pounds of push, upwards
Here, Hawkeye (The Avengers) applies 300 Newtons (70 pounds) of force, pulling the bowstring towards him.
A force vector needs both the direction and magnitude (amount of pull) in order to be fully described.
Distance and displacement – not the same thing
Distance (scalar) – how much ground you covered while walking.
Displacement (vector) – how far you end up, compared to where you started.
Let’s see distance vs displacement in action
Motion is relative
There’s no such thing as absolute speed.
Speed only has meaning when its measured relative to some fixed point.
Don’t believe me? How fast is this cannonball moving?
Did it stand still? (and then fall)
Or was it moving at 50 miles/hour? (and then fell)
Both! It depends on whether we measure its speed relative to the car (negative 50 miles per hour), or its speed relative to the ground, 0 miles/hour.
Now get ready for an even more amazing example:
Using kinematics in music videos
How fast are you moving, right now?
Moving…compared to what – to the floor?
You may be standing still.
But compared to the center of the Earth, you’re rotating around the Earth’s circumference.
Compared to the Sun, we’re revolving around it at a high speed, and so on.
Consider these animations by Yathish Dhavala
Interactive flash animations PCCL Click ‘frames of reference’
How fast is the Earth moving around our Sun?
Average distance from Earth to the Sun = 149,597,890 km
Assuming that Earth revolves around Sun in a circle (approx),
it travels 1 circumference per year.
velocity = distance/time
velocity = 2π(149,597,890)km / year
Given 365 days/year, 24 hours/day, we then obtain
velocity = 107,300 km/h (67,062 miles per hour)
Orbiting the Galaxy
Our Galaxy is in spinning motion, like an enormous pinwheel…. we can focus on the speed of the Sun around the center of the Milky Way Galaxy5.
It takes our Sun approximately 225 million years to make the trip around our Galaxy. This is sometimes called our “galactic year”. Since the Sun and the Earth first formed, about 20 galactic years have passed; we have been around the Galaxy 20 times.
On the other hand, in all of recorded human history, we have barely moved in our long path around the Milky Way.
How fast do we have to move to make it around the Milky Way in one galactic year? It’s a huge circle, and the speed with which the Sun has to move is an astounding 483,000 miles per hour – 792,000 km/hr
The Earth, anchored to the Sun by gravity, follows along at the same fantastic speed.
Speed = distance / time
Examples: 10 meters/second, or 50 miles/hour
Velocity = distance/time , direction
Examples: 10 meters/second , north
Average Speed versus Instantaneous Speed
During a trip to school, your car changes its speed.
Speedometers show the speed at a particular instant in time.
Don’t confuse this with average speed.
Average speed is a measure of the distance traveled in a given period of time.
During a trip to school, you traveled 5 miles.
The trip lasted 0.2 hours (12 minutes)
So the average speed is….
There may have been times that you stopped,
and others that you went 50 miles per hour.
But on average you moved at 25 miles per hour.
PowerPoint: Linear Motion, Hewitt Conceptual Physics
- Motion is relative, Speed, Velocity, Acceleration, Free fall
Animations of 1-Dimensional Kinematics
Kinematic graphic analysis
Open these documents (Word, Google Docs)
2016 Massachusetts Science and Technology/Engineering Standards
HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
PS2.A Forces and motion. How can one predict an object’s continued motion, changes in motion, or stability?
Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
Introductory Physics. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.
1.1 Compare and contrast vector quantities (e.g., displacement, velocity, acceleration force, linear momentum) and scalar quantities (e.g., distance, speed, energy, mass, work)
1.2 Distinguish between displacement, distance, velocity, speed, and acceleration. Solve problems involving displacement, distance, velocity, speed, and constant acceleration.
1.3 Create and interpret graphs of 1-dimensional motion, such as position vs. time, distance vs. time, speed vs. time, velocity vs. time, and acceleration vs. time where acceleration is constant.
Learning Standards: Common Core Math
- Common Core Math
- CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable
- CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
- CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.