What is Kinematics: Definition and 1000 Discussions

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.
Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. They are also central to dynamic analysis.
Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.

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  1. J

    I Momentum, impact force and Earth

    Suppose two objects, A and B, with large lengths LA and LB, and masses MA and MB, collide at time t0. Both objects before collision are vertical and aligned concentrically, being object B positioned initially at a higher z coordinate than object A. The bottom end of object A is rigidly...
  2. C

    I Forward kinematics of a snake robot

    i want to build a forward kinematic model of a snake robot, to find its end-effector position am already worked on a few robotic arms like puma 560 using the DH table so i tried using the DH table on the snake robot, but it seemed wrong, so how do i do it ? the snake robot is similar to the...
  3. Eobardrush

    Ball rolling down a slope problem: Find an expression for time taken

    Question: Galileo released a metal ball from rest so that it could roll down a smooth inclined plane. The time t taken to roll a distance s was measured. He repeated the experiment, each time recording the time taken to travel a different fraction of the distance s. Write an expression for the...
  4. F

    Relating Linear and Angular Kinematics

    a) We use the definition of linear speed in terms of angular speed: v = r*omega omega_f = v/r = (1.25 m/s)/(0.025 m) = 50 rad/s omega_0 = v/r = (1.25 m/s)/(0.025 m) = 21.55 rad/s b) We use the definition of linear speed: v = d/t d = vt = (1.25m/s)(74 min)(60 s/1 min) = 5.55 km c) We use the...
  5. Physics_learner

    Kinematics - can't find the initial velocity according to the image

    I tried to write the data I understood from the image: y0=160m yf=0 x0=0 x1=192m I tried to express the total change in time using the position over time equation on the Y direction: y(t)=y0+v0y*(t2-t1)-0.5a(t2-t1)^2 but then I stuck with 2 variables and didn't know what to do any help?
  6. PhysTeacher88

    B Misleading Textbook Equation for vf^2=vi^2 + 2ad

    The textbook (Nelson 11) at my school lists the "big 5" equations for uniform acceleration. In all but one, they use vectors. For vf^2=vi^2 + 2ad, the opt not to use vectors. Is there a deep reason why we would not want to use the vectors? I understand that when you square the velocity, the...
  7. Mjusttheletter

    100m dash kinematics problem

    So what I have done is that on question 7 I know he is accelerating to constant my knowns are that it is from initial and acceleration is given so I have that for my first phase the second phase is that Your vfinal is your new initial for it and acceleration is the constant but you don't know...
  8. Stewkatt

    2D kinematics -- Calculate the acceleration of the jumping athlete

    this is my work but the answers say 11 m/s^2 so I made an error somewhere. Also if someone could help me with solving the direction for the acceleration, that would be greatly appreciated.
  9. knapklara

    Simple kinematics question -- Riding a bicycle race in two different gears

    I calculated average velocity but obviously it helps nothing with this problem. I hope to get me going with these exercises once I break the ice. Thank you in advance!
  10. vibha_ganji

    Halliday Resnick Krane Chapter 2 Problem 30: Juggling Five Balls

    If each ball rises two meters, then the time is in the air is equal to around 1.28 seconds. After this, what am I supposed to do? I feel really stuck. If all of the balls are released at different times, how am I supposed to find the answer?
  11. brochesspro

    Roundtrip by Plane: Understanding Wind & Velocity Effects

    The question I have is that if the aero plane is traveling in the same direction as the wind, would it not increase its velocity, as in with boats and streams? So, if by chance, ##w = v##, then the velocity of the aero plane would double. It feels weird as going by the same logic, if the speed...
  12. ayans2495

    Kinematics and One Dimensional Motion

    Would we assume that the deceleration of both instance are the same?
  13. N

    Compensating for Earth's Rotation With v = ωr

    We know that ##v = \omega r## where ##r = R_{\text{E}} + h##. To compensate for the motion, the plane must fly along the equator at the same speed as the Earth but in the opposite direction, i.e. from east to west, so $$\vec{v} = -\vec{ v}_{\text{E}}$$ $$v_{\text{E}} = \omega_{\text{E}}...
  14. F

    I Kinematics cases with non-constant acceleration

    Hello, I understand that, for 1D kinematic problems where the acceleration function ##a_x## is initially given along with the initial conditions, we can use calculus (differentiation and integration) to get the position ##x(t)## and velocity ##v_x (t)## of the moving object. When the...
  15. Istiak

    Find equation of motion of an inclined plane when there's friction

    It's the body. So there's friction on that plane and there's tension also. $$L=\frac{1}{2}m_1\dot{x}^2+\frac{1}{2}m_2\dot{x}^2-m_2g(l-x)-m_1gx\sin\theta$$ $$f=\mu N=-\mu m_1 g\dot{x}\cos\theta$$ I had found the frictional force's equation from [the...
  16. WMDhamnekar

    MHB What are the Kinematics of a Particle?

    I hope the following questions relating to heading of this thread belongs to this forum.
  17. Einstenio

    Motion of a Particle: Solutions & Examples

    This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that there is an constat vector 'a' that satisfy a•r=constant, than the motion would be on the surface of a cone. So i tried to make...
  18. Einstenio

    I Classical Mechanics - Motion of a particle

    Show that a point with acceleration given by: a=c*((dr/dt)×r)/|r|3 where c is a constant, moves on the surface of a cone. This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that...
  19. J

    Kinematics chasing problem: Car vs. Motorcycle acceleration question

    Im for some reason getting 1.58 s for time. I found 1.75 m as the head start distance and then I do d=d so: 2.45t^2 = 1.75t^2 +1.75 but the answer for "a" should be 6.45s...
  20. J

    Kinematics Chasing Problem: Correct Answer and Explanation

    I solved this and got 27.3 seconds so basically what I did was found the headtsart of the slower car (15.6 m/s times 6.65 seconds) but the answer given is 33.9 seconds and it uses the second (faster cars speed) to find the head start distance. Which answer is correct and why? Thanks so much
  21. Afo

    Confused while reading HRK regarding rotational kinematics

    Pic 1: Pic 2:
  22. O

    Car passing two markers, kinematics question

    i calculated the time difference between each marker, and using the first equation, i solved for V1. i then used this V1 as V2, time as the first marker (3.75) and used the second equation to solve for V1. is this method correct? can somebody please verify?
  23. S

    2-D kinematics challenge problem help please

    Hi! I can't solve this. Please someone give me a hint and help? I'm unsure what equation to use. Thank you!🙏🙏🙏 An artillery crew demonstrates its skill by firing a shell at an angle of 49 deg and then lowering the gun barrel and firing a second shell at a smaller angle of 20 deg in such a way...
  24. brochesspro

    What is the speed of the bicycle?

  25. L

    Kinematics: two runners with different and non-constant accelerations

    1. $$x_{A}(t)=\begin{cases}\frac{1}{2}a_A t^2 & 0\leq t\leq 2.8\\ \frac{1}{2}a_A 2.8^2 +v_A t & t>2.8\end{cases}=\begin{cases}\frac{1}{2}a_A t^2 & 0\leq t\leq 2.8\\ \frac{1}{2}a_A 2.8^2 +a_A\cdot 2.8\cdot t & t>2.8\end{cases}$$ so ##x_A(5)=40## implies ##a_A=\frac{40}{17.92}m/s##. Similarly for...
  26. 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...
  27. P

    Kinematics problem -- Calculating where a dropped stone will hit a car

    0=6-4.9(t^2) 0=-27,7t+Xo From the first equation, T= 1.10s From the second equation, (Xo/27,7)=t 0=6-4.9((Xo/27,7)^2) We solve for Xo = 30,65 Now, we have X=-27,7t+30,65 If t=1,10 Then , -27,7(1,10)+30,65=0,18 which is not equal to 0. Which means the stone hits the ground first. Is my answer...
  28. H

    Building a Two Omni Wheel Robot: Questions & Answers

    Hello! I have a somewhat complicated robot project that I've simplified here to hopefully get a quick answer. I want to build a robot with two omni-wheels that looks like the following (not drawn to scale), where the black is the omni wheels at 45 degree angles and the blue is the robot body...
  29. C

    Types of Kinematics: Classical, Quantum & Relativistic

    I was taught that kinematics is the study of local motion without references to its causes (like forces, fields, etc.). That seems useful to say but perhaps it is not really that helpful. What are the kinds of kinematics? I can think of three kinds: classical kinematics (from mean speed to...
  30. uranium92

    A Graph analysis problem to find when the acceleration is zero

    I had deduced that B,E,H are the places where acceleration will be zero, but when I read the solutions it showed that K also has a = 0. It said it had maximum slope and then said a = 0. But I couldn't understand why? Please help.
  31. Prez Cannady

    A Question about extragalactic stellar motion

    We have direct mass models of stellar motion inside of galaxies (basically, find a happy medium between a sphere and a disc). And of course dark matter corrections to explain the deviation between model and observation. Is there any pattern at all to the motion of extragalactic stars passing...
  32. V

    How Does the Angle Theta Affect the Velocity Calculation in String Problems?

    The way I tried to solve it is by using following reasoning. The inclined part of the string will each have a speed of U m/s. So the point P just above mass M where the inclined strings meet is being moved up by each inclined string at ##U \cos {\theta} ##. Therefore, the speed of the point P...
  33. V

    Determine time after which 4 persons meet in given scenario

    The point of confusion is deciding the direction each persons sets out in i.e. velocity direction of each person. Knowing this will probably help in getting the solution. At t=0, I can say that velocity of each person is as shown in diagram below.
  34. P

    Solving a Vector Triangle Differential Equation

    By considering a vector triangle at any point on its circular path, at angle theta from the x -axis, We can obtain that: (rw)^2 + (kV)^2 - 2(rw)(kV)cos(90 + theta) = V^2 This can be rearranged to get: (r thetadot)^2 + (kV)^2 + 2 (r* thetadot)(kV)sin theta = V^2. I know that I must somehow...
  35. anthonywsadler

    Simple Work Problem Disagreeing with Kinematics

    I have the following problem: "A box with a mass of 10 kg is accelerated by 10 m/s/s over a distance of 10 meters. What is the kinetic energy of the box (assuming no friction)" Using work... Work = K.E. F * D = K.E. m*a*D = K.E. = 10 kg * 10 m/s/s * 10 m = 1000 Joules However, using...
  36. E

    Kinematics: Analyzing circular motion of a particle

    Help please
  37. lion1014

    Grade 12 Kinematics -- Will the car stop before the cliff?

    t= v/a =25.8 m/s / -2.5 m/s^2 =10.1 s therefore, d= vi * t + 1/2at^2 = (25.8)(10.1) +1/2(-2.55)(10.1)^2 =131 m I got the first one right I think, but I don't know how to do b
  38. R

    Unreasonable values for engine torque in vehicle simulation

    I'm trying to simulate the physics of a Toyota Camry during acceleration with a time granularity of 100ms. My simulated conditions are as follows: m = 1590 kg v = 17 m/s a = 1.5 m/s2 η (transmission efficiency) = 0.85 rwheel = 0.35 m Fdrag = 100 N Ffriction = 260 N Faccel = 1590 kg × 1.5 m/s2 =...
  39. wcjy

    Conservation of energy, centripetal acceleration, kinematics

    (a) Using COE, $$mgh = 0.5mv^2 + 0.5I\omega^2$$ I solved it, where $$\omega = 112 rad/s$$ (b) This is the part where I have question or problem. I saw my course mate working and he start of with finding centripetal acceleration. $$a_c = \frac{v^2}{r} = \frac{(r_0\omega)^2}{R_0}$$ Why isn't it...
  40. O

    How to find d2 when given d1 and d, total time, and average velocity?

    I rearranged the displacement formula to d2 = d + d1. I used cosine law to solve for d2 since the triangle is not right-angled but I am not getting the correct answer or angle for d2. The angle I used in cosine law (based on the diagram) was 32+12+90 = 134. d = v(t) = 130(3) = 390 km/h [N 32 E]...
  41. J

    Seemingly Simple Kinematics Question

    Hello, Perhaps I am overthinking this, but I am trying to find the acceleration of the 'pulse rate' in the below plot. Every so many seconds there is a pulse (you can think of this as x displacement). The initial rate between pulses is 5 pulses/sec (you can think of this as velocity). I am...
  42. Amrator

    Relativistic Kinematics: Distance of B When A Coincides with L

    I don't know why I'm so puzzled by this problem; it's only one star. So first, I drew a picture of A and B in the ground frame. Then I drew B and the ground in A's frame. I then used the velocity addition formula to obtain the velocities of both B and the ground relative to A. $$\frac{v_{B}^{A}...
  43. fingerprintregion

    Relativity: Relativistic Kinematics and Dynamics

    I’ve read Beiser’s Modern Physics Chapter 1 and I am able to grasp the general theories but not so much when applying it to problems. I major in Chemistry and would really appreciate any head start/help/suggestions. For number 1 I thought of using L = L0 sqrt 1-v^2/c^2 but can’t seem to find the...
  44. dudu

    Kinematics Question: A motorboat and a log in a stream

    I found vlog=1.9/t and vb-v=1.15/t and vb+v=d+1.15/60.8 don't know what to do now
  45. N

    Kinematics question: Stunt driver jumping his car from ramp to ramp

    Do i use the equation above mentioned to solve it? If i do, am i correct to say that Vx = 90/3.6 cos 30 and Vy = 90/3.6 sin30?
  46. wcjy

    Kinematics, Conservation of energy, momentum

    m1 + m2 = 8 COE 0.5(m1)(u1)^2 + (m1)(g)(30) + 0.5(m2)(u2)^2 + (m2)(g)(30) = 0.5(m1)(v1)^2 + 0.5(m2)(v2)^2 + (m2)(g)(16) Can you check if my eqn is correct? And can you advise what to do after this? I wanted to do COLM but i don't know what is the initial part.
  47. AN630078

    Kinematics Motion with Variable Acceleration

    The displacement of the particle is; s= ∫v dt s= ∫4-3t^2 dt s=4t-t^3+c When the particle is at the Origin, t=0; 0=4(0)-(0)^3+c c=0 So this becomes; s=4t-t^3 The particle next passes through the origin when; 4t-t^3=0 Factor out the common term -t; -t(t^2-4)=0 Rewrite t^2-4 as t^2-2^2 and factor...
  48. Kitanov

    Finding Trajectory of x & y in Kinematics

    I need to find a trajectory x = 4cos(2t) + 3sin(2t) y = 3cos(2t) - 4sin(2t)
  49. aspodkfpo

    An error made in a kinematics question about a spring launcher?

    Genevieve the galah wants to test out her new creation - the Nifty Numbat Launcher. It consists of a large, ideal spring with equilibrium length l1 = 1.7 m and spring constant k=41 N/m. The spring rests upon a ramp of length l1 inclined at an angle β=30∘ to the horizontal. The spring is attached...
  50. Ashelion

    Kinematics Question with weird units

    Would the A = 2.0 ms^(-5/2) affect my answers for parts (a) to (c)? Since I basically ignored the unit ms^(-5/2) and integrated the function to get the ones for velocity and displacement. And as for part (d) explain the dimensions of A; I assumed that the ms^(1/2) comes from the square root due...
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