Acceleration Definition and 1000 Threads

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. George Plousos

    I A version of the twin paradox without accelerations

    Bob is standing on Earth and Alice is on a distant planet at a constant distance from Earth. Their watches are already synchronized in the following sense: Suppose Alice's planet is a light-year away from Earth. Bob emits a light signal to Alice at time t = 0 according to Bob's watch. When Alice...
  2. J

    Why is there angular acceleration in a non-spinning gyroscope?

    I was watching the above video which is part of a series explaining the mechanics behind a gyroscope. In the video the author explains the mechanics of the gyroscope when stationary (the disc is not rotating). Here he derives a result that the angular acceleration is g/r which is non zero...
  3. Leo Liu

    A particle moving with zero radial acceleration in polar coordinates

    In the example above, the authors claim that when ##r=r_0e^{\beta t}##, the radial acceleration of the particle is 0. I don't quite understand it because they did not assume ##\beta=\pm \omega##. Can anyone please explain it to me? Many thanks.
  4. A

    I Solve Constant Acceleration Problem in Special Relativity

    Basically I just want to work out a constant acceleration problem in relativity, of the same kind of introductory physics. Vo= 0.9999c Vf = 0 D= 50 Au Accel, Earth frame? Accel, Ship frame? Time of transit, Earth frame? Time of transit, ship frame? Motion is 1-D. All origins line up at the...
  5. Kaguro

    What is the issue with the polar acceleration problem?

    ##\vec r=r \hat r## ##\vec v=\dot r \hat r + r \dot \theta \hat \theta## ##\vec a = (\ddot r - r \dot \theta^2)\hat r + (2 \dot r \dot \theta + r \ddot \theta)\hat \theta## Given that, ##2 \dot r \dot \theta + r \ddot \theta =0## Also, ##r \theta=constant## ##\Rightarrow \dot r \theta + r \dot...
  6. Amitkumarr

    To find the Acceleration of a Pentagonal metallic plate

    In order to find force( and hence the Acceleration) on the Pentagonal plate,we must find the Resistance of the plate.But to find the resistance we must know how the current is flowing through the given plate(see attached figure). My question is how is the current flowing through the Pentagonal...
  7. Selfphysicslearner

    What is wrong with following physics equations? (velocity and acceleration)

    vavg=(Vi+Vf)/2 vavg=h/t then vavg*t=h h=(Vi+Vf)/2 * t Vf=at (Vit+at2)*1/2=h But formula on every resource I found says it should be; (Vit+at2*1/2)=h What mistake did I do ?
  8. T

    Apparent weight of a body with upward acceleration

    I initially attempted to get the answer by multiplying the mass by 50, as I assumed if the upward acceleration was 5g then the weight could be found by just multiplying the mass by the acceleration of 50ms^-2. However that resulted in an answer of 3750 which was far below the correct answer of...
  9. LCSphysicist

    Doubt about vector acceleration

    Say... A ball is moving to the right, and we want to say that it doesn't slip. My doubt is, in which case we put Vrot = - Vcm = - α*r or Vrot = Vcm = α * r
  10. ttesss

    Newton's 2nd Law: Force, Mass and Acceleration

    I´m currently studying Newtons 2nd law and I don't get how can force only depend on mass and acceleration and not on velocity.. I mean, if I punch something with my fist going at constant velocity ( acceleration=0) it stills has a force right?
  11. Dman0500

    Dynamic Equilibrium -- Acceleration of a rock thrown from a bridge

    I know the acceleration of the rock is equal to g, but why. If we neglect air resistance, what is actually making the rock fall? Wouldn't it be that g overcomes the acceleration of the y plane at some point so the rock starts coming down or in this case accelerate more by throwing below 0 degrees?
  12. G

    Acceleration issue -- A 120W motor starts to lift a load of 20 kg....

    Okay, here is a question I just can't solve. The 120W motor starts to lift a load of 20 kg. During which time, this load will reach a speed of 0.5 m / s, taking into account the potential energy. PS: Ignore losses in the mechanism!
  13. I

    When calculating a car's acceleration, is it ok to substitute Torque?

    1. When calculating a car's acceleration, is it ok to substitute Torque into a= F/ma= F/m T= FrF= T/rwhere a= acceleration, F= force, m= mass, T= Torque, r= radius,a= T/rm ?
  14. O

    Angular Rotation and Acceleration

    [Mentor Note -- OP deleted his posts after receiving help. His posts are restored below] @ocean1234 -- Check your messages. Deleting your post is not allowed here, and is considered cheating. Problem was given: ##\theta(t) = at - bt^2 + ct^4## a) calculate ##\omega(t)## b) calculate...
  15. jamiebean

    The final velocity = initial velocity + acceleration x time

    I first calculated initial velocity: √7.09^2+1.07^2=7.17028 acceleration=√7.22^2+2.47^2= 7.63 then i substituted all values into this equation: final velocity=initial velocity + acceleration x time so, final velocity=82.0285 so the magnitude= final velocity-initial velocity= 74.858271 is...
  16. M

    Exploring Moment of Inertia & Angular Acceleration for Drone Propellers

    Hi, I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...
  17. R

    Exploring Circular Motion: Centripetal Acceleration

    Hey guys, Theres something I've been confused about when looking at circular motion. When does an object have just centripetal acceleration as the acceleration of the object, if ever. I think that the acceleration vector is between the centripetal and tangential acceleration when an objects...
  18. Adesh

    What actually is the centripetal acceleration formula?

    Centripetal force is defined as the force causing the body to follow a curved path, acting towards the center and always orthogonal to the direction of motion. For uniform circular motion the formula for centripetal acceleration is $$a_c = \frac{v^2}{r}$$. But my understanding of centripetal...
  19. K

    Help with acceleration -- A block on top of a block on a frictionless table

    I don't understand the problem. Does not block A and B make a system, so they should have the same velocity and acceleration at all time? If not, why do they have different accelerations? I don't understand this part of the problem either: "pull applied to block B equals 12.0 N, then block B has...
  20. L

    Mars Rover Upthrust and Acceleration calculations help 🚀

    1. ρmars atmosphere = 0.02 kgm^-3 volume of a sphere = 4 / 3 𝜋 𝑟^3 gmars = 3.8 ms^-2 So: Volume of a hemisphere=2/3 𝜋 𝑟^3 r=7.75 m Archimedes' principle states that the upthrust on an object is equal to the weight of fluid that the body displaces To find the upthrust produced...
  21. M

    Finding the 'g-force' of a decelerating falling mass.

    Hey all, I need a reality check and verification on some work I have been doing. I feel as though I might be too close to the problem now and am missing something about this. It's also been a few years since I studied physics at University, so I'm a little rusty. Problem: An initially...
  22. karush

    MHB Acceleration @ $\dfrac{5\pi}{4}: \sqrt{2}$

    $\tiny{299}$ For $t \ge 0$ the position of a particle moving along the x-axis is given by $v(t)=\sin t—\cos t$ What is the acceleration of the particle at the point where the velocity is first equal to 0? $a. \sqrt{2}$ $b. \, —1$ $c. \, 0$ $d. \, 1$ $e. —\sqrt{2}$Ok well originally it was...
  23. Jorrie

    I Has the evidence for anisotropy of cosmic acceleration been discussed?

    I have searched the forum a bit but could not find a discussion of this Astrophysics letter: 'Evidence for anisotropy of cosmic acceleration', Jacques Colin et. al, 18 Oct 2019. Can someone please direct me to any forum discussion?
  24. VVS2000

    Compound pendulum experiment to find the acceleration due to gravity

    In this experiment, I still can't figure out why the graph between time period and distance from point of oscillation is like that. Why does it first decrease and increase so steeply? I got the second part because it goes near the centre of gravity and time period becomes almost infinite there...
  25. cpgp

    Finding the angular acceleration of a flywheel

    I have solved part a using the conservation of energy, getting a (correct) answer of 47.9 km/h, but I am unable to make headway with part b. Based on the flywheel rotating at 237rev/s when the car is moving at 86.5 km/h, I obtained omega = (237*2pi)v/24=62v. Differentiating both sides should...
  26. S

    About acceleration and mass....

    Now, if I recall correctly, lighter objects with smaller inertia do go faster in terms of acceleration and farther than objects with heavier mass or inertia when the same force is exerted on them. But what about same accelerations? If a light object and a heavy object were to undergo the same...
  27. lua

    Solving Spool Acceleration Problem Using Newton's Laws

    I solved this problem using second Newton law for translational motion and the same law for rotational motion, and got $$a= \frac {F} {m+ \frac {I} {R^{2}}} (cosϕ−rR)$$ where m is spool mass. Now, we have three cases: (a) ##cos\phi>\frac{r}{R}##, when spool is accelerating to the right, (b)...
  28. Parkerrhees

    Electromagnetic fluid acceleration as effective rocket propulsion?

    Let me preface this by saying I have no background in physics or any of the above other than hours and hours of reading. Could someone explain why (if a method was developed) we couldn't use EFA as a thrust system for a rocket? My reasoning is instead of using fuel to fight gravity and push...
  29. G

    SR w/ Acceleration: Distance Measured by A

    Well, using (1) is easy to see that, at a given time in C ##t## both curves are described with the same value of ##\tau##, i.e. ##\tau_A=\tau_B=\tau##. So the corresponding positions at a given time ##t## are $$x_{AB}=x_{0,AB}+\frac{\cosh{(a\tau)}-1}{a}$$ and therefore $$\Delta x \equiv x_B -...
  30. danielhaish

    Question about acceleration and movemenr

    But we know it not true becouse then it was almost impossible to run on a train
  31. RoloJosh16

    Find the initial acceleration in a system

    Let´ s call ##N_x## the magnitud of the force between the rod and the box and ## N_y## the magnitud of the force between the rod and the surface. ##N_x = ma_c## ##N_x= ma_r## ##mg-N_y=ma_y## The following I think is to find a relation between ##a_r## and ##a_y## and that can be found by...
  32. Sakyo107

    Finding the Average Acceleration

    Hello, so I am working on a projectile motion lab but I'm not sure what to do right now. Essentially, the lab consisted of my classmates and I using an air table to show that the vertical and horizontal components of projectile motion are independent. During one of our trials, we placed a puck...
  33. jamiebean

    Is Gravitational Acceleration Positive or Negative in Upward Motion Problems?

    I attempted the question with d=vi x t + (at^2)/2 gravitation acceleration= -9.8 and I got the solution of 22.724. Should I use the value of -9.8? or should I just use 9.8? should I use the equation above? I feel like what I am calculating is not displacement but distance... thank you
  34. simo22

    Finding motion where the acceleration depends on position and time

    I have computed that the acceleration in my problem is a(t) = -gj - k/m(|r(t)| - L_0) * r(t)/|r(t)| Where a(t) is the acceleration vector, g is the gravitational acceleration, j is the unit vector in y-direction, k is the spring constant, m is the mass, r(t) is the position vector, |r(t)| is...
  35. xWaldorf

    Unraveling the Mystery of Mass and Acceleration

    So, this may be a really stupid question, and I strongly feel as though I'm missing something here. How can it be that objects of different masses have the exact same acceleration when mass is in fact resistance to acceleration? And then, if in (a vaccum) I throw upwards M and m ( a bigger and a...
  36. Vortex8380

    Mechanics problem — Car moving with constant acceleration

    I tried this but I don't know if it makes sense: Average velocity from A to B = 22/2 = 11m/s Average velocity from B to C = 104/4 = 26m/s (26-11)/6 = 3.75m/s
  37. M

    Velocity / Acceleration Diagrams of a Mechanism - Piston and a rotating rod

    Summary:: This is a question about finding the acceleration of a point in a mechanism Hi, I have a question about the mechanism shown in the attached picture: Question: We are told that \omega = 6 rad/s and the first part is asking me to find the acceleration of point P on the piston when...
  38. K

    Accelerometer with a Charge: Measuring Acceleration?

    Suppose we have an accelerometer carrying a charge. The charge density everywhere in the instrument is uniform, or at least what I mean to say is, the charge on any component is proportional to that component's mass. Now, in an inertial reference frame, we place the accelerometer in an electric...
  39. R

    Maximum Acceleration: I Got the Correct Answer

    I got the correct answer which is √g. I solved it as if it were a circular motion with radius of 1. But got no idea why my solution did work.
  40. Yalanhar

    Acceleration of a moving wedge with a falling block

    When the box travels a ## X## distance, the wedge travels ## \frac{X}{2}##. So ##a = 2A## Using the wedge as a non inertial frame: I didn't use (4). Using (2) on (3) and then on (1) I got: ##2mA=mgsin\alpha +mAcos\alpha + \frac{-mgcos\alpha sin\alpha +mAsin^2\alpha +MA}{2cos\beta -...
  41. R

    Angular Acceleration: Understanding the Relationship Between Connected Pulleys

    Hi everyone I had this argument with someone told. About angular acceleration. His opinion: Since both pulleys are connected by a string then both of them must have the same angular acceleration. My opinion: Since a2 "acceleration of the second mass" is half a1. Then angular acceleration of the...
  42. B

    Radial acceleration derivation with minimal knowledge

    Just started learning about uniform circular motion. I really don't understand how we get aΔt2/2 on the side. I also searched on the internet for a similar derivation, but there are none so simple. Thanks for your help! P.S There is a mistake in calculation in second line (textbook error).
  43. R

    Calculating the spring displacement response from an acceleration input

    I'm working on a project where we have a mass (50 kg) sitting on a spring (350 N/mm) and are subjecting it to a sudden impulse (20g) along the spring axis to simulate a shock. We have the profile of the acceleration defined as: ##a(t) = x''(t) = P\cdot \sin^2 (\pi \cdot t / T)## Where P (peak...
  44. S

    Motorcycle at max lateral acceleration

    In the case where ground clearence isn't the limiting factor; Since motorycles are steered using countersteering, a motorcycle cornering at constant max g can achieve any decrease of lean angle (bringing the bike up) by turning harder towards the inside of the turn momentarily, which is not...
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