Relative motion Definition and 282 Threads

The relative velocity







v
→




B
∣
A




{\displaystyle {\vec {v}}_{B\mid A}}
(also







v
→




B
A




{\displaystyle {\vec {v}}_{BA}}
or







v
→




B
rel
⁡
A




{\displaystyle {\vec {v}}_{B\operatorname {rel} A}}
) is the velocity of an object or observer B in the rest frame of another object or observer A.

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  1. MatinSAR

    Relative Motion: Understanding the Relationship Between Moving Objects

    My attemp : ##\vec r_1## : Position of the river in reference frame. ##\vec r_2## : Position of the walker in reference frame. ##\vec r_x## : Position of the walker measured by the river. We have: $$\vec r_1 + \vec r_x = \vec r_2$$ $$\vec v = \dfrac {d \vec r}{dt} $$ $$\vec v_1 + \vec v_x =...
  2. C

    B Question about the relative motion of an eye relative to light source

    Hello everyone, I've been thinking about 2nd postulate of relativity, it seems that and the Michaelson-Morley experiment seems to imply that there is no ether, but I was thinking about a special situation that doesn't seem to go against that postulate. I think my question is basic so hopefully...
  3. apcosta

    What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?

    TL;DR Summary: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis? a) Consider two rigid bodies that have a relative motion characterized by a rotation and a translation with respect to the same axis (like a bolt and a...
  4. Aayush Verma

    Effect of relative motion on pressure of gas in a container

  5. Islam Hassan

    B Is Time Defined by Relative Motion in SR and GR?

    We only measure time via the relative movement of a standard, agreed reference, a clock for example. If we replaced all instances of "time" in the formulation of SR and GR by "relative motion [ie, of an agreed reference]", would SR/GR remain correct/consistent? Or does SR/GR rely on a deeper...
  6. Shreya

    Kids on a merry-go-round & Relative Motion

    (Please refer the image below. ) The velocity of Nick ##v_N=\omega r## and the velocity of John ##v_S=\omega R## is depicted. The relative velocity of Nick with respect to John will be ##v_{NJ} = \omega (R-r)##. The velocity is along the tangent to the circle centred at B. If Nick were to move...
  7. M

    B What if a needle hits Jupiter at nearly speed of light?

    This is much like the "grain of sand" at near speed of light hiting Earth, but now targeting Jupiter with a needle! What if... Any way, which is the correct way to analyze this kind of scenarios? For example, I think than being the speed of the needle near c, is nonsense to think about the...
  8. MatinSAR

    Relative motion with constant acceleration

    I think the question is wrong. My answer : But it should be wrong because : I think the question is wrong … But I'm not sure …
  9. unoonu

    Relative Velocity Against the Water Current

    vcanoe_wrt_ground = 3 m/s + (-6) m/s = 3 m/s - 6 m/s = -3 m/s Thus, if I understand this correctly, the rower will never reach his goal 36 m away as his canoe's resultant velocity is negative (i.e., his canoe is effectively going downstream even though it is trying to go upstream). My only...
  10. M

    I Relative Motion vs. 'Relative' Acceleration: Twin 1 & 2

    Given the relativity concept between twin 1 and twin 2 what is the difference between relative motion and 'relative' acceleration? Are not either twin experiencing the differential between them as a consequence of acceleration. When twin 1 instigates motion relative to twin 2, a moving carriage...
  11. MD LAT 1492

    I Relative Motion & Local Frame’s Position - when projecting components

    Does the position of the origin for the body’s rotating coordinate frame 1) stay fixed to the moving body or 2) does it stay fixed to the inertial frame, yet still able to rotate as the body rotates with the only restriction that it cannot translate with the body i.e. only affixed at the...
  12. G

    Did I Miss Something in Disputing a Popular Book's Solution on Relative Motion?

    I do not agree, this is bullocks. We can simply set up position vector of ##\vec A(t)## and ##\vec B(t)## with respect to the fixed center of the carousel, their relative velocity is simply ##\frac{d (A-B)}{dt}## or ##\frac{d (B-A)}{dt}## Since this is a pretty popular book, I am wondering if I...
  13. R

    Relative Motion Comparing my motion vs an airplane

    I'm having trouble understanding the plane one This is what I understand so far v I'm sitting at a chair right now and if I compare my relative motion to the ground my relative velocity would be 0m/s but if I compare my motion to the solar system I would be moving very fast. I just can't grasp...
  14. J

    Special Relativity - relative motion of two bars

    Hi, I'm stucked in this exercise. I don't know how to proceed. Any hints I appreciate it.Two bars of the same proper length L, moves in the same way on the x axis. In the referential of one of the bars the time interval between the events, when the extremity right of one bar and the extremity...
  15. M

    Equations of relative motion with respect to a rotating reference frame

    Hi, I am just writing a post to follow up on a previous thread I made which I don't think was very clear. The question is mainly about how to use the below equations when there is also a rotation of the body around the fixed reference point. Please see the diagram here to see how the vectors...
  16. A

    I Is a Merry Go Round Floating in Space an Inertial Frame of Reference?

    its a short question...
  17. C

    How to Find the Path Function and Meeting Time for Three Moving Particles?

    Velocity of B wrt C = (v +v*cos 60) i^ - vsin60 j^ = (3v/2)i^-((3)^(1/2)/2v)j^ But since C is also moving this initial velocity would vary. So how to find a function which defines its path and hence I can find time at which the particles meet. I was told to take rotating frame of reference that...
  18. R

    I Special Relativity: Comparing Lengths in Parallel Motion

    In Introduction to special relativity by Resnick,there is a thought experiment to compare lengths perpendicular to relative motion as given in the below image. What if we try to perform such an experiment to compare lengths parallel to relative motion? Suppose there are two horizontal rods...
  19. Like Tony Stark

    Find the angle so that it seems that Mars is approaching to you

    I know that ##v_{M/S}=v_M - v_S##. I also know that ##v_M = (-24.1;0)##. Then, using some trigonometry, ##v_S=(-19.3 sin 30°;19.3 cos 30°)##. So I can find ##v_{M/S}##. But that doesn't tell me anything about the angle ##\beta##.
  20. Like Tony Stark

    Body connected to two parts of a rope on an inclined plane

    The thing is that my professor said that if the velocity of ##A## is ##400 cm/s##, the velocity of ##B## is ##200 cm/s## because "##B## is connected to two parts of the rope and ##A## is conected just to one part", and he also said that that ##200 cm/s## is the velocity of ##B## with respect to...
  21. Like Tony Stark

    Find the force needed for a body on an inclined plane to be static?

    Here, I have two doubts 1) if the surfaces are frictionless, then there's no force being applied on the ##x' axis## of ##m_1## except from the weight, so it should be sliding, shouldn't it? So, there's no force that I could apply to ##m_2## to keep ##m_1## in equilibrium since any force that I...
  22. Like Tony Stark

    Measuring position, velocity and acceleration in relative motion

    Well, ##r(t)## in ##A## is just a vector ##(0;y)## because is tangent to the trajectory. Then, from the perspective of ##B## the particle moves in an uniform circular motion. Is this right? The velocity from ##B## must be ##\omega##, right? And what about acceleration?
  23. Like Tony Stark

    Pulley system with relative motion

    Well, first I tried to understand the relation between the velocities and accelerations of both bodies and I got that the velocity of ##B## is half the velocity of ##A##. This is because a change in length of the cord "that touches ##A##" must be equal to the change in length of the two cords...
  24. Like Tony Stark

    Particle moving in a rotating disc

    Well, I tried plugging the data in the formula. I know that ##\vec a_b = 0; \vec \omega=3 rad/s ; \vec r## can be calculated using trigonometry. Then I also know that ##v_{relx}= 10 cm/s##, ##a_{relx}=15 cm/s^2##, ##\vec {\dot{\omega}}=-10 rad/s^2##. But how do I get ##v_{rely}## and...
  25. Like Tony Stark

    Spaceship approaching Mars and relative motion

    As the problem asks for the spaceship's perspective, I know that I should take ##\vec v_S=0## and ##\vec v_M=24.1-19.3## because the motion is relative to the spaceship. Then, the relative velocity of Mars and ##SM## should have the same direction. If they have the same direction, that angle...
  26. Like Tony Stark

    Relative rotational motion on a disc

    The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. ##\vec a_B=0## because the origin isn't accelerated, ##\vec{\dot...
  27. Santilopez10

    Relative motion between cars with different types of movements

    I think my approach is quite wrong, still I gave it a shot: First I know that ##v_A=13.3 m/s=r\omega=60\omega \rightarrow \omega=0.2 \frac{rad}{s}## Then $$\vec a_A=-r\omega^2 e_r=-2.4 e_r$$ But ##e_r=\cos{\theta}i+\sin{\theta}j## and substituing the latter in the acceleration equation I have...
  28. adosar

    B Time Dilation & Relative Motion: Who Measures Proper Time?

    Consider the example of flashing light in spaceship. The observer in the spaceshipe and the observer in the Earth measure different times. Both observers could argue that the clock of the other tick slower(motion is relative). But is anyone right ? I mean the one will measure proper time...
  29. gibberingmouther

    Relative Motion of Charges Question

    This problem seems pretty simple but I don't understand how the correct answer is 500,000 smaller than what I calculated. You have an electric field that has a magnitude of 10^6 V/m in the positive z direction. I assumed (though it was not stated) that the cause of this field was a sheet of...
  30. jha192001

    Magnetic Field and a Charged Particle -- relative motion question

    Here's a experiment. There is a magnetic field vertically downward and a charged particle is kept inside it. Simple. Does it experience a force? Now if we move a speed of 2m/s relative to the frame of rest charged particle. Then it must experience a force right?(Becuz now its velocity is not...
  31. Alexanddros81

    Determine the ground speed and the course of the plane

    Homework Statement 15.1 The airspeed of the plane is 200m/s, directed north. If the wind speed is 30m/s in the direction shown, determine the ground speed and the course (angle θ) of the plane. Homework Equations The Attempt at a Solution Is it so far correct the above? More questions...
  32. H

    Problem using vectors and relative motion

    Homework Statement A river of width 4 km flows at 5 km/h. A swimmer whose speed relative to water is 4 km/h, starts swimming from a point A on a bank. What minimum distance will the swimmer have to walk on the other bank to reach point B directly opposite to A? [/B]Homework Equations Vba = Vb...
  33. J

    B Relative motion and proper time

    Hi everyone! Sorry for the bad english! Quick question Just to see if I understood: If a person on a spaceship moving at 0.7c in relation to a person in the earth, and both of then agreed they started making microwave popcorn at the same time (like when the spaceship is just above the head of...
  34. J

    B Why Does Vqp Need to be Tangential to Vq in Order for Q to Get Closest to P?

    https://www.physicsforums.com/attachments/221718 Say if we have two particles P, and Q, traveling at velocities Vp and Vq respectively. If it is IMPOSSIBLE for Q to collide with P, let us find the distance of closest approach. So from the frame of reference of P, itself is stationary, and Q is...
  35. Captain Levi

    What Is the Speed of the Man Relative to the Ground?

    Homework Statement If a river is going 6 km/hr relative to the ground, a boat is going 14 km/hr relative to the river, and a man is jumping from one end of the boat to the other at 6 km/hr relative to the river. What is the speed of the man relative to the ground? I'm stuck between the...
  36. P

    Kinematics -- flying a plane in the wind to a destination

    Homework Statement A plane is taking off from an airport directly west of the airport it wishes to touch down in. The plane in still air can travel with a constant speed of 730 km/h. If a wind is blowing constantly at 92 km/h [45° S of E], at what angle must the plane fly to compensate for the...
  37. J

    Relative motion of converging objects

    If two objects are traveling on paths at 90 deg to each other such that they will converge at a point how do we describe that motion. For example 2 cars are approaching a 4 way intersection and will collide. They see each other as moving diagonally yet when they collide one will t-bone the...
  38. E

    B Synchronize Clocks in Relative Motion: How & Why

    Is there any way to synchronize two clocks already in relative inertial motion? If so, how? And I am not sure exactly what “synchronize” would mean in that context. Maybe it would mean that their readings, or at least their running rates, would match when their relative motion was stopped? There...
  39. M

    What is the angle and displacement of the plane?

    Homework Statement In the figure below, a radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is d1 = 412 m at 40° above the horizon. The airplane is tracked for another 123° in the vertical east–west plane, the range at final...
  40. P

    Voltage due to relative motion of a charge and conductive loop

    Consider an electric charge Q with rest frame R and a closed conductive loop L with rest frame R'. Q is moving relative to L, and vice versa. In R, the loop is moving and receives no magnetic flux from Q thus no voltage according the integral form of Faraday's law. In R', the loop receives...
  41. R

    Relative motion of two observers

    Homework Statement Two observers having identical instruments carry out identical experiments to study the motion of a massive particle. First observer concludes that the particle is moving in a straight line with constant velocity while the second observer concludes that the particle is moving...
  42. EspressoDan

    I Relative Motion vs Time: Paradox Explained

    Hi, I'm reading a book explaining relativity. I previously understood the subject in layman's terms but am now confused. The author has introduced relative motion in an invariant universe with the concept that motion through space is only relative to the observer. Given this, I'm now...
  43. S

    Relative motion problem with airplane and wind velocity

    Homework Statement A small airplane wants to fly from A to B which is 200 km due south. The wind is blowing towards the east at a velocity of 50 km/h. If the airplane can move through the air at 300 km/h, find the direction the plane should be heading; the speed of the airplane relative to the...
  44. L

    Derivation of Rocket Equation Using Relative Velocity

    Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...
  45. P

    What is the Correct Direction of Hay Bales in a Basic Relative Motion Problem?

    Homework Statement A farmer is throwing bales of hay off the back of his tractor with a speed of 3 m/s relative to the tractor, which is moving west with a speed of 7 m/s. Determine the speed and direction of hay bales relative to the ground. Homework Equations subtract the speeds, since they...
  46. H

    Relative Motion: Calculating the Angle for Accurate Newspaper Delivery

    Homework Statement Homework Statement A newspaper boy throws papers sideways onto the porches of his customers while riding his bicycle along the sidewalk. The sidewalk is 15m in front of the porches. The boy throws the papers at a horizontal speed of 6m/s relative to himself, and rides the...
  47. T

    How Fast is the Airplane Flying Relative to the Air?

    Homework Statement After flying for 15 min in a wind blowing 42 km/h at an angle of 31° south of east, an airplane pilot is over a town that is 50 km due north of the starting point. What is the speed of the airplane relative to the air? Homework Equations Vx of wind=42km/hr*cos(31) Vy of...
  48. nysnacc

    Understanding Relative Motion in Circular Motion

    Homework Statement Homework Equations a= omega^2*r The Attempt at a Solution a_A/B = a_A - a_B a_A = 10^2*r (-î) a_B = 10^2*r (+ĵ) a_A/B = 10^2*r (-î) - 10^2*r (+ĵ) => -200 î -200 ĵ why is the answer 200 î -200 ĵ (accelerate in +î direction) ?
  49. nysnacc

    Calculating Sailboat Relative Motion with Equations and Conversions

    Homework Statement Homework Equations v_theta = r * theta_dot 1 knot = 1852 m The Attempt at a Solution v_0 = 6 * (1852m/h) * (1/3600 h/s) = 3.087 m/s
  50. A

    Minimum distance between bomb and shell

    1. Prolem Statement:- An aircraft is flying horizontally with constant velocity = ##200 m/s##, at a height = ##1 km## above the ground. At the moment shown, a bomb is released from aircraft and the canon- gun below fires a shell with initial speed = ##200 m/s##, at some angle #\theta#. 1)For...
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