What is Acceleration: Definition and 1000 Discussions

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time.
Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes:

the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force;
that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.The SI unit for acceleration is metre per second squared (m⋅s−2,






m

s

2







{\displaystyle {\tfrac {\operatorname {m} }{\operatorname {s} ^{2}}}}
).
For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during circular motions) acceleration, the reaction to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or orthogonal during circular motions) acceleration, the reaction to which the passengers experience as a centrifugal force. If the speed of the vehicle decreases, this is an acceleration in the opposite direction and mathematically a negative, sometimes called deceleration, and passengers experience the reaction to deceleration as an inertial force pushing them forward. Such negative accelerations are often achieved by retrorocket burning in spacecraft. Both acceleration and deceleration are treated the same, they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in reference to the vehicle.

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  1. Huzaifa

    B Understanding Galileo's Theory of Acceleration

    I am not able to understand the following paragraph from my Physics textbook; "The velocity of an object, in general, changes during its course of motion. Should it be described as the rate of change in velocity with distance or with time? This was a problem even in Galileo's time. It was first...
  2. D

    Is Fgy the Same as FN in a System with Two Masses and Friction?

    I am just confused on how to find the normal force/ FN of the first object. My classmates are saying Fgy is the exact same as Fn but I don’t get why Fgy= Fg sin theta Fgy= (20)(9.81) (sin35) Fgy= 112.5 Fgy = FN
  3. rxhim631

    Average acceleration of an arrow by a bow

    Distance= (Intial Velocity + Final Velocity / 2) Time 0.75 = (0+75 / 2) Time 0.75 = (37.5) Time 0.02 seconds = Time Acceleration = (Final Velocity + Intial Velocity) / Time Acceleration = (75 - 0) / 0.02 Acceleration = 3750 m/s2 Idk if this is correct can someone help pls.
  4. M

    I The Acceleration and the density of galaxies

    In the Lambda-CDM model, the density of galaxies goes decreasing and should even vanish in the far future. I would be grateful if someone could point me to a paper where this is calculated.
  5. Gannet

    I Acceleration of Universe Expansion: 1/r2

    It seems to me as the space between galaxies expands it reduces the gravitational attraction between them. Assuming that this is happening between the majority of the galaxies in our Universe it would cause the acceleration of expansion by a factor of 1/r2.
  6. nick26

    Measure angular velocity and acceleration from missing tooth wheel

    Hi, I need to come up with a math model for a digital ignition system. I've been thinking about it and I think that I need to measure 2 things to be able to calculate when I have to start charging the coil. They are the angular velocity and the acceleration but how can I do it? the idea is to...
  7. C

    I Non-uniform Circular Motion & Acceleration

    I would really appreciate some help with this problem regarding non-uniform circular motion, in which a body is accelerating as it follows a circular path. If we take Example 1, a body starts at Point A with an angular speed of 180°/s. The body accelerates to Point B and reaches it some time...
  8. CPW

    Acceleration in Polar Coords, Intuitive Definition video

    Summary:: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:
  9. 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.
  10. R

    Calculating Track Acceleration Due to Gravity

    The force is driving the rotation is gravity. My question is that what is the track acceleration? How do I calculate it?
  11. potatotimer

    A steel shuttle is pulled along a rail, what is its initial acceleration?

    it sounds like you just need to use F/m = a which gives 25 / .76 = 32.89 = a this didn't work so I tried to get the x component of acceleration so I did 32.89cos(45) = 23.26 and this didn't work. what am I missing, the force is tension right so it should be 25N?
  12. J

    Orbital mechanics: is ballistic capture possible without acceleration?

    All spacecraft that have been put into orbit around other planets have required engines to decelerate them and inject them into their orbits. So-called "ballistic capture", from what I've read, always seems to call for at least a minimum application of force to change the trajectory; I get...
  13. boniphacy

    A Deriving Acceleration in Gravity from E = mc^2

    I want to derive an acceleration in the case for a stationary mass in the gravity field. I found the total energy in the GR is provided by a simple equation: https://en.wikipedia.org/wiki/Schwarzschild_geodesics ## E = mc^2\sqrt{1 - rs/r} * \gamma ## So, this is easy to provide acceleration...
  14. Pipsqueakalchemist

    Engineering Zero Velocity & Acceleration of Point of Contact: Problem Explanation

    For this question the ball is rolling without slipping so that means the velocity of the point of contact is zero. Does that also apply to the acceleration of the point of contact? Because that’s what I assumed and I applied the relative acceleration formula above and use the starting point to...
  15. P

    Stewart-Tolman Effect (Current caused by Acceleration of wires)

    Consider the inertial reference frame in which the positive ions forming the crystal lattice of some portion of a metallic ring are at rest. In this frame, an inertial force of mra exists. Consider the electrons in this portion of the metallic ring. The inertial force of mra is exerted on the...
  16. Pipsqueakalchemist

    Engineering Rigid wheel rolling without slipping -- Trying to find angular acceleration

    So I tried the problem and it’s different from the solution. I’m confused on why my attempt didn’t work, is it because the wheel is undergoing general planar motion? I tried to just apply Newton’s 2nd law to find the acceleration of the centre and then use that to find angular acceleration. The...
  17. cianfa72

    I Is acceleration absolute or relative - follow up

    Hello, Some doubt arose me reading this thread https://www.physicsforums.com/threads/is-acceleration-absolute-or-relative-revisited.999420/post-6454462 currently closed. Sorry, I have not be able to quote directly from it :frown: Your claim is not , however, asserting that the spacetime...
  18. G

    Engineering Acceleration Engineering First Semester

    The function x (t) = 4 (m · s) t − 1 + 10 m describes the position of a mass point. In which direction does the speed point at time t = 1 s? Is the amount of speed constant or not? does the velocity function change its sign for t> 0 at some point? And in which direction does the acceleration...
  19. J

    I How does a particle's acceleration relate to the emitted photon?

    I understand that any accelerating charged particle will emit a photon. But I do not understand how the rate of acceleration relates to the photon that is emitted. For example: If a proton is falling to Earth in a vacuum at 9.8 m/s^2, then what are the characteristics of the photon that will be...
  20. barryj

    Calculating max acceleration of a Tesla car

    [Mentor Note: Two threads with similar titles merged] First calculate the equivalent force on the car from the max torque. An average tire is 15 inch diameter = about .2 meter radius Since T = F X R , F = T/R = 660/.2 = 3300 Newtons. since F = M X A, A = F/M = 3300/2083 = 1.6 m/sec^2...
  21. L

    I Acceleration in special theory of relativity

    In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?
  22. P

    Centripetal acceleration problem (box sitting on a table)

    Let me imagine a box placed on a table. It has got no acceleration. If I were a person who trusted Newton's laws then I would argue that the net force on the box should be zero. Now in another situation I am an observer outside the Earth and I see that the box is rotating along with the earth...
  23. F

    Constant acceleration in a rocket

    I thought I'd start by writing the problem in a tensor formalism. I have identified with ##S## the Earth and ##S'## the rocket. Since the acceleration provided is in the rocket's frame of reference, I can write the following four-vector. $$ a'^\mu=(0, a, 0, 0) $$ Since we are interested in the...
  24. C

    Automotive Need help calculating load torque and acceleration torque of a vehicle

    Hi everyone, I'm working on designing a vehicle that uses electric motors, but I'm having a little trouble finding the load and acceleration torques in order to select the right motors to use. Variables: m = total mass of vehicle a = acceleration μ_r = rolling friction coefficient r = wheel...
  25. guyvsdcsniper

    What are the units for the slope in an Acceleration vs Mass Graph?

    I am doing an Atwood Simulation lab. I am having trouble with this part of my lab that ask the question provided. I can tell that the relationship is linear and that as the mass increases at a constant rate the acceleration increases. Logger pro tells me that the slope is 31.43. I am having...
  26. S

    A question about humans and acceleration

    I have been wondering, and curious as well, and thus I would like to ask: Generally, are acceleration as in reaching top speed or zero speed from top speed and acceleration in terms of changing direction equally easy for human beings at average and normally, or is changing speed easier than...
  27. R

    Finding Acceleration of a Car Where Crumpling Occurs (Momentum)

    80km/h = 22.2 m/s Through momentum: 1940(v_f) = 540 (22.2) + (1400)(-22.2) => v_f = -9.84 m/s I figured the work that the energy lost in a collision is equal to the work done to crumple the cars. So W = K_i - Kf = [1/2 (540)(22.2)^2 + 1/2(1400)(-22.2)^2] - 1/2(1940)(-9.84)^ 2 = 384110 J At...
  28. LCSphysicist

    Proper time in an acceleration frame

    $$d\tau = \sqrt{-g_{\mu v}\frac{dx^{\mu}}{d\lambda} \frac{dx^{v}}{d \lambda}} d \lambda $$ Calling ##d \lambda = d t##, t is coordinate time in an inertial frame. $$\Delta \tau = \int \sqrt{-(-1+v^2/c^2)} dt$$ $$\Delta \tau \approx \Delta t - \frac{g^2*\Delta t^2}{6c^2}$$ where $$\Delta t = 2...
  29. S

    Acceleration of objects connected by pulley on rough inclined plane

    Summary:: Please see the picture below Let say: ##W_1## is weight of ##m_1## ##W_2## is weight of ##m_2## ##f_1## is friction on ##m_1## ##f_2## is friction on ##m_2## I want to find the acceleration of the system. Since I don't know in which direction they will move, I just assume ##m_1##...
  30. yucheng

    Incorrect derivation of tangential acceleration in polar coordinates

    I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...
  31. B

    What is the angle between the acceleration and velocity when rotating?

    ##ω = \frac {k} {\sqrt{φ}}## What is the angle between acceleration and velocity after 1spin (2π radians)? First I decided to find out what is the angular acceleration: ##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = -...
  32. dahoom102

    Getting the angular velocity using the angular acceleration graph

    The answer here is A What i did is getting the area as follows, 2×4×1/2 +3×-6×1/2 +4×-6 = -29 and then use this Δω=ωf-ωi -29=ωf-5 ωf=24 but there is no such choice.
  33. I

    Grade 11 Question: Newton's Third Law -- Calculating acceleration of an airboat

    for c) i need help d) Given: Let [forward] be positive. F 1 = — 250 N F 2 = 360 N Unknown: a = ? Equation: F net= F1+ F2 F net= m a Solve: F net= (— 250 N) + 360 N = 110 N F net= m a a = F net/ m = 110 N / 220 kg= 0.5 m/s [forward] Statement: The acceleration of the boat is 0.5 m/s [forward].
  34. P

    I Is acceleration absolute or relative - revisited

    Hello all, I just joined this group after stumbling over a post from 2003 on this topic. The issue I'd like to deal with is the spinning bucket of water and why the water will still climb up the sides of the bucket if the bucket is stationary. In the original post an Absolutist put it like...
  35. S

    Acceleration of U-pipe containing water

    I am thinking of using ΣF = m.a to find the acceleration but I don't know what causes the resultant force to the right. I thought it will be the difference in pressure on the left and right leg of the U-pipe (picture on the right), which is ΔP = ρ.g.h but the force (ΔP . A) won't be directed to...
  36. V

    Circular motion of a particle around a track -- what provides the centripital acceleration?

    Suppose a particle is moving around a circular track of radius R at speed v. To bend around a circle some agency has to exert an acceleration towards the center of the circle. I analyze the forces acting on the particle, its weight and the normal force and there is no acceleration in the...
  37. F

    A Radial acceleration for spherically symmetric systems in GR

    Hello, I was reading few papers discussing modified gravity theories and their use in understanding galaxies with no dark matter by checking for anomalous velocity dispersion. Now, the author was using 4 gravity theories MOND, Weyl, MOG and Emergent gravity. The thing is he had provided the...
  38. naviakam

    How Does Compressing Fully Ionized Gas Accelerate Ions to High Energies?

    Fully ionized gas, if compressed to a cylinder of mm scale, collapses rapidly and accelerates the e/ions to very high energies (MeV). The temperature in the compressed gas is around 100 eV. What could be the possible acceleration mechanism?
  39. duchuy

    Determine the acceleration of a puck on an inclined air hockey table

    Hi, I'm struggling to start this exercice, where I have an inclined air hockey table with an angle alpha. They gave me this chronophotography (this is online) saying that the ratio is 1:1 I really don't know how to proceed since this is online and I'm thinking if I measure this with a ruler...
  40. C

    Maximum acceleration given a breakable edge

    Using Newton's second law, $$ cos\left( \frac{\pi}{6} \right) m(a+g) = 150 \Leftrightarrow a = \frac{\frac{2\times 150 }{\sqrt{3}}-mg}{m} =4.633. $$ Unfortunately, the possible answers are A. 1.025, B. 0.625, C. 3.75, D. 2.75, E. 1.75, F. 0. What am I getting wrong? Isn't the force exerted on...
  41. I

    Acceleration of rising mass and tension in cord

    First I determined the direction the masses will be traveling by comparing the change in potential energy, so when M2 rises by Δy, M1 drops by Δy. Potential energy decreases when M1 drops and M2 goes up. Tension force for string pulling against M1= 400 x gsin30°, and since there are two strings...
  42. Leo Liu

    Confusion about the derivation of acceleration relative to rotating frames

    This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...
  43. mattlfang

    Find the velocity and acceleration of a pulley in a mass-spring system

    This looks like a classical setup but I can't find a solution. We can calculate the energy of the system by looking at the work done by the gravity and the spring. But how do we divide the energy between the kinetic energy of the pulley and the rotation of the pulley?
  44. E

    I Relativistic Velocity, Perp. Accel., Momentum: Explained

    A stationary observer sees a particle moving north at velocity v very close to the speed of light. Then the observer accelerates eastward to velocity v. What is its new total velocity of the particle toward the north-west relative to the observer? I ask because while the particles total...
  45. Rafums

    How to calculate acceleration of blobs in any degree pendulum?

    I want to create a method to calculate acceleration of blobs in any degree pendulum (double, triple and more). I have this equation but I am not sure if it is correct, or how to extract acceleration from it. [Mentor Note -- this is a new thread start to correct errors in the previous 2 thread...
  46. brotherbobby

    Pendulum hung from the ceiling of a train

    (a) No, a person seated inside the train compartment will not be able to tell whether the train is accelerating on a horizontal track or moving uniformly up an inclined track by observing the plumb line. (b) I am assuming that both observers are not allowed to look "out" of the boundaries of...
  47. J

    Angular Momentum Problem: Determining Angular Acceleration

    So I first tried to find L using torque, Torque=d/dt*L, and took the integral of this. Ended up with 23.28484t Now I square the equation L=rotation rate*I to get L^2=rotation acceleration *I^2 Angular acceleration=L^2/I^2 I feel like I am doing something wrong though, this doesn't give the...
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