<< Chapter < Page Chapter >> Page >

Making connections: relativity and einstein

Because Einstein was able to clearly define how measurements are made (some involve light) and because the speed of light is the same for all observers, the outcomes are spectacularly unexpected. Time varies with observer, energy is stored as increased mass, and more surprises await.

Phet explorations: motion in 2d

Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle).

Motion in 2D


  • Velocities in two dimensions are added using the same analytical vector techniques, which are rewritten as
    v x = v cos θ size 12{v rSub { size 8{x} } =v"cos"θ} {}
    v y = v sin θ size 12{v rSub { size 8{y} } =v"sin"θ} {}
    v = v x 2 + v y 2 size 12{v= sqrt {v rSub { size 8{x} } rSup { size 8{2} } +v rSub { size 8{y} } rSup { size 8{2} } } } {}
    θ = tan 1 ( v y / v x ) . size 12{θ="tan" rSup { size 8{ - 1} } \( v rSub { size 8{y} } /v rSub { size 8{x} } \) } {}
  • Relative velocity is the velocity of an object as observed from a particular reference frame, and it varies dramatically with reference frame.
  • Relativity is the study of how different observers measure the same phenomenon, particularly when the observers move relative to one another. Classical relativity is limited to situations where speed is less than about 1% of the speed of light (3000 km/s).

Conceptual questions

What frame or frames of reference do you instinctively use when driving a car? When flying in a commercial jet airplane?

Got questions? Get instant answers now!

A basketball player dribbling down the court usually keeps his eyes fixed on the players around him. He is moving fast. Why doesn’t he need to keep his eyes on the ball?

Got questions? Get instant answers now!

If someone is riding in the back of a pickup truck and throws a softball straight backward, is it possible for the ball to fall straight down as viewed by a person standing at the side of the road? Under what condition would this occur? How would the motion of the ball appear to the person who threw it?

Got questions? Get instant answers now!

The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger’s frame of reference. Draw its path as viewed by a stationary observer.

Got questions? Get instant answers now!

A clod of dirt falls from the bed of a moving truck. It strikes the ground directly below the end of the truck. What is the direction of its velocity relative to the truck just before it hits? Is this the same as the direction of its velocity relative to ground just before it hits? Explain your answers.

Got questions? Get instant answers now!


Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. (a) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45º size 12{"45º"} {} south of east. What was his total displacement? (b) Allen encountered a headwind averaging 2.00 m/s almost precisely in the opposite direction of his motion relative to the Earth. What was his average velocity relative to the air? (c) What was his total displacement relative to the air mass?

(a) 35 . 8 km size 12{"35" "." 8" km"} {} , 45º size 12{"45º"} {} south of east

(b) 5 . 53 m/s size 12{5 "." "53 m/s"} {} , 45º size 12{"45º"} {} south of east

(c) 56 . 1 km size 12{"56" "." 1" km"} {} , 45º size 12{"45"º} {} south of east

Got questions? Get instant answers now!

A seagull flies at a velocity of 9.00 m/s straight into the wind. (a) If it takes the bird 20.0 min to travel 6.00 km relative to the Earth, what is the velocity of the wind? (b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km? (c) Discuss how the wind affects the total round-trip time compared to what it would be with no wind.

Got questions? Get instant answers now!

Questions & Answers

What is conductivity
Saud Reply
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
how to find magnitude and direction
Arjune Reply
how to caclculate for speed
derivation of ohms law
Kazeem Reply
derivation of resistance
R=v/I where R=resistor, v=voltage, I=current
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Electric current is the flow of electrons
Kelly Reply
is there really flow of electrons exist?
Yes It exists
explain plz how electrons flow
if electron flows from where first come and end the first one
an electron will flow accross a conductor because or when it posseses kinectic energy
electron can not flow jist trasmit electrical energy
free electrons of conductor
electric means the flow heat current.
Serah Reply
electric means the flow of heat current in a circuit.
What is electric
Manasseh Reply
electric means?
electric means the flow of heat current in a circuit.
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
Jenny Reply
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
why we cannot use DC instead of AC in a transformer
kusshaf Reply
becuse the d .c cannot travel for long distance trnsmission
what is physics
Chiwetalu Reply
branch of science which deals with matter energy and their relationship between them
Life science
what is heat and temperature
Kazeem Reply
how does sound affect temperature
Clement Reply
sound is directly proportional to the temperature.
how to solve wave question
Wisdom Reply
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Just know d relationship btw 1)wave length 2)frequency and velocity
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
nice self promotion though xD
thanks dear
hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
please guys help, what is the difference between concave lens and convex lens
Vincent Reply
convex lens brings rays of light to a focus while concave diverges rays of light
for mmHg to kPa yes
it depends on the size
Matthew Reply
please what is concave lens
a lens which diverge the ray of light
concave diverges light
thank you guys
A diverging lens
What is isotope
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
what is wire wound resistors?
Naveedkhan Reply
Practice Key Terms 5

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?