# What is Linear acceleration: Definition and 76 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.

View More On Wikipedia.org
1. ### I Sagnac gyroscope affected by linear acceleration?

As some of you know I have been coding a 2+1D relativistic simulator that can handle (constant proper) acceleration in any direction on a plane. So far it is going quite well. I have now decided to simulate a Sagnac gyroscope inside the simulation by sending signals in opposite directions...
2. ### Finding linear acceleration of a spool and cable

My angular acceleration is wrong but all I had done was torque which was 110 NM / I = 930 kg-m^2 and calculated 0.118 rad/s^2. But because this is wrong I am stuck and I have no idea how to find angular velocity to plug into the equation to find linear acceleration.
3. ### Kinematics Problem: constant acceleration, motion in a line

I've been attempting to solve this problem for three days now. I have thrown away my old attempts (like, scrumpled up into the bin), but my old attempts involved: Trying to set up simultaeneous equations relating the journeys between EH and FG to find the deceleration, but the reason why this...
4. ### Torque required at the wheels to accelerate a vehicle at a certain rate?

I'm struggling to understand something basic here. If I have a just a wheel, with mass 10kg, and radius 0.25m, and I specify that the CG is accelerating linearly at 1ms-2, how do I calculate the force needed to do this? Using F = ma gives 10N, but using this value for torque calculation on the...
5. ### Linear acceleration by using Magnetic strips

I am working with Magnetic strips to get countinous force in both clockwise and anticlock wise direction. I am looking for better concept for hand free mode in my experiment. The pdf file of my experiment is attached .
6. ### I Colliding black holes: when will linear acceleration end?

I was musing about black hole mergers and what an observer might see for a particularly simple (i.e. blatantly contrived) scenario. Suppose that there are two (non rotating, un-charged, bog standard) black holes of dissimilar masses heading for a head-on collision. They will accelerate towards...
7. F

### Ball rolling down an incline angular and linear acceleration

Homework Statement A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration? Homework Equations Fnet= ma T = F x r T = IO’’ a = rO’’ The Attempt at a Solution Fnet = mgcos(O) - FfT = FfrT = IO’’ Ffr = bmr^2O’’ Ff =...
8. B

### Tangential acceleration, linear acceleration, and torque

What is the difference between tangential and linear acceleration of a circular object (let's say a ball)? Also, how does the torque contribute to linear acceleration?
9. J

### What do the values represent in this equation?

Homework Statement Hi everyone. I did an experiment in my house where I took four different geometric circles to represent a solid sphere, a spherical shell, a solid cylinder, and a hoop. I rolled all the objects down an incline of about 8 degrees, took video footage, uploaded into the tracker...
10. ### What is the relation between angular and linear acceleration

I am wondering, when solving rigid body exercises, how can I express the relationship between linear and angular acceleration for a general case? E.g. what would be the linear acceleration in function of the angular one of a 1m rod that is rotating through a fixed point 0.6 m away from its mass...
11. ### Find the linear acceleration of points on a rolling cylinder

Homework Statement [/B] A uniform cylinder with radius r is rolling down an incline without slipping as shown in diagram below. It's angular acceleration is α and acceleration of it's center of mass C is a. What will be the linear acceleration of point of contact P and another point Q on the...
12. ### Frames of Reference: Linear Acceleration View - Comments

kuruman submitted a new PF Insights post Frames of Reference: Linear Acceleration View Continue reading the Original PF Insights Post.
13. ### Linear acceleration, Angular acceleration, tension.

Homework Statement A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s. Mass of wheel: 3kg Outside rad. of gyration of wheel: 300mm Radius of gyration: 212mm calculate: (a) The linear acceleration of the...
14. ### B Calculating Linear and Angular Quantities from Applied Force

In the image above, a centroid with radius 1 is depicted. F1 is pointing directly at point A (which is the center of the circle), and F2 is pointing directly at point B. The radius for finding the torque would be the perpendicular between the center of the object and the force vector, so r1...
15. ### Calculate linear acceleration of a pivoted stick

Homework Statement A uniform thin stick of mass M and length L has a moment of inertia about its centre of mass of I = (1/12)ML^2. The stick, which is pivoted at one end, is held horizontal and then released. Assuming the pivot is frictionless, calculate: i) the linear acceleration of the free...
16. ### Nonuniform Linear Acceleration

Homework Statement Refer to figure. Homework Equations v=ds/dt → ds=vdt a=dv/dt → dv=adt ads=vdv The Attempt at a Solution I tried taking the derivative of the given position function. Then I am kind of lost from there.
17. ### I Is this Linear Accelerator Design Valid?

Good Evening Everyone, A group of friends and I were having a mini-contest, to see who could theoretically make anti-matter using the most simplistic design in terms of cost and general complexity. The obvious choice for us was the Positron, due to low energy requirements on all fronts. One of...
18. ### Rotational Vs Linear Acceleration

Hi guys, I'm having a debate with a mechanical engineer friend of mine, and I was wondering if you could help me solve it. I'm not much of a physicist, but honestly I think he might have this one wrong, I just can't remember my old physics classes well enough to calculate and be sure. The...
19. ### Rolling without slipping & linear acceleration vector

Homework Statement Rolling without slipping A) Derive the linear acceleration vector equations for points A, B, C, and O in terms of R, ω, α and θ at this instant. B) R = 0.5 m, ω=-54 r/s and α = 0. Determine the MPH of the vehicle and the vector accelerations of points A, B, C, and O. C) R...
20. ### Finding angular acceleration of pulley attached to a mass

Homework Statement A block of mass 2kg (mb) can slide down a frictionless 53 degree inclune, but it is connected to a pulley of mass 4kg (mp with a radius of 0.5m. The pulley may be treated as a disk. What is the angular acceleration of the pulley? Homework Equations a = rα The Attempt at a...
21. ### Linear Acceleration Homework: Equations & Solutions

Homework Statement Homework Equations ac = v2/r The Attempt at a Solution I know for circular motion. The radial acceleration is always towards center and tanegntial acceleration is perpendicular to it. But here for rotational motion... The question asks about linear acceleration.. Is it...
22. ### Difference between centripetal and linear acceleration?

Hello all! I'm having some difficulty understanding one of the concepts of angular motion. My textbook tells me that the total linear acceleration of a point in a rotating body is the vector sum of tangential acceleration and centripetal acceleration. However, later on in the chapter, there is...
23. ### Determine the linear acceleration of the two masses

Homework Statement Two masses, mA = 40.0 kg and mB = 55.0 kg, are connected by a massless cord that passes over a pulley that is free to rotate about a fixed axis. This device is known as an Atwood’s Machine. The pulley is a solid cylinder of radius R = 0.360 m and mass of 7.50 kg. 1...
24. ### Resultant linear acceleration at the rim of a disk

Homework Statement A uniform disk with radius 0.390m and mass 27.0kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to θ(t)=( 1.50rad/s)t+( 9.00rad/s2)t2 . What is...
25. ### Simple finding linear acceleration

Homework Statement In our lab, we times a cart going 1m. The time was 9.49 s. The cart was pulled by a string, over a pulley, attached to a free-falling mass. The purpose was to calculate the μ, the coefficient of friction. Homework Equations d = vit + 1/2at^{2} a = (vf-vi)/t...
26. ### Distance from non-uniform linear acceleration

I have an object at rest which accelerates at a variable rate before coming to rest again. At any given point I can determine it's linear acceleration, accounted for gravity. I would like to determine the distance traveled between the 2 resting points. I understand some of the pieces...
27. ### I have a big doubt. Is centripetal acceleration linear acceleration?

It is generally said that centripetal acceleration is directed towards the center of the circular path along the radius. So can we say that centripetal acceleration is a linear acceleration. Is it or can it be represented along a straight line. I had a question in my exams. A kid is rotating a...
28. ### Linear acceleration and rotational motion

Homework Statement You are the technical consultant for an action-adventure film in which a stunt calls for the hero to drop off a 20.0-m-tall building and land on the ground safely at a final vertical speed of 4.00 m/s. At the edge of the building’s roof, there is a 100-kg drum that is...
29. ### Linear speed and magnitude of linear acceleration

Homework Statement A car with 64.0-cm-diameter tires is being driven down a level road at 75.0 km/hr. As seen by a person riding in the car (i.e. relative to the passenger), what are the linear speed and magnitude of the linear acceleration of a) the center of one of one of the wheels, b) a...
30. ### Linear acceleration with letters instead of numbers

Homework Statement A lift starts from rest and travels with constant acceleration 4 m/s^2.It then travels with uniform speed and comes to rest with constant retardation of 4 m/s^" The total distance traveled is d and the total time taken is t. Show that the time spent traveling at a constant...
31. ### Linear acceleration question

A passenger train, which is traveling at 80 m/s is 1500 m behind a goods train which is traveling at 30 m/s in the same direction on the same track. At what rate must the passenger train decelerate to avoid a crash? My attempt at the question: V=u+at 0=80+at a=-80/t I tried to find at...
32. ### Rod on a pivot: Linear acceleration and reaction forces

Homework Statement Homework Equations r * \alpha = atan r * \omega^2 = arad The Attempt at a Solution arad = (L/2)(3g/L) = 3g/2 atan = (L/2)(3g/2L) = 3g/4
33. ### I need to find a velocity for a given t value, from a linear acceleration graph

Homework Statement A particle move along the x-axis, each starting with V = 10 m/s at t = 0 seconds. Find each particle's velocity at = 7.0 . Work with the geometry of the graphs, not with kinematic equations. Homework Equations A(t) = {10t +10, 0 ≤ x ≤ 2 -10t+30, 2 < x ≤...
34. ### Angular and Linear Acceleration on a Wheel

Homework Statement A 68 cm diameter wheel accelerates uniformly about its center from 150 rpm to 270 rpm in 4.1 s. 1. Determine its angular acceleration. α = 3.1 rad./s^2 2. Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.6 s after it has...
35. ### Calculating Torque and Linear Acceleration of a Rotating Rod

Homework Statement A uniform rod of mass M and length L is free to rotate about a pivot at the left end. It is released from rest in the horizontal position ( Thetha=90 degrees). What is the torque on the rod when it makes and angle (theta) with the vertical? What is the downward linear...
36. ### What is linear acceleration in uniform circular motion?

What is "linear acceleration" in uniform circular motion? Yesterday, I took an exam and it was asked a concept that we hadn't studied, at least in the way it was written. The exercise explained that a circular motion was decreasing its velocity, and we had to be able to identify which of the...
37. ### Linear acceleration on a rotating body

What is the difference between tangential and radial acceleration for a point on a rotating body? As far as I know, the tangential acceleration changes the magnitude of the linear velocity of the point and the radial acceleration changes the direction of its linear velocity. But I don't...
38. ### Linear acceleration of a rod fixed to a hinge at one end

Homework Statement a uniform stick with a mass of 1.00 kg and length of 1.00m has a fixed hinge at one end. It is released at an angel of 60 degrees above the horizontal and it drops with normal gravity. What is the magnitude of the linear acceleration of the point at the free end just after...
39. ### Solving linear acceleration for time.

I'm currently developing a program which solves the displacement of an object using the standard acceleration equation [d=i*t + 0.5*a*t^2], where i=initial velocity, t=time and a=acceleration. As the need has arisen to determine the time at which an object reaches a particular displacement...
40. ### Finding an expression for linear acceleration of a hanging mass

A rope of negligible mass is wrapped around a uniform solid cylinder, of radius R, that can rotate freely about its axis, which is horizontal and fixed. A block hangs vertically from the rope and causes the cylinder to spin. The blocks mass, M_B is 4 times the mass, M, of the cylinder. Find an...
41. ### Torque to linear acceleration.

Urgent! Torque to linear acceleration. Please Help! Homework Statement Q1: A horizontal force F=1000N is applied on a 120kg fridge as shown below. If friction is present, what is the magnitude of the fridge linear acceleration, and the magnitude of the normal forces acting at A and B? (hint...
42. ### Falling Chimney, Angular and Linear Acceleration

Homework Statement R = 49 m theta = 29° Homework Equations Kinematic equations for Rotational Forces and Circular motion Kinetic Energy = 1/2*I*w^2 The Attempt at a Solution First I can find the moment of Inertia for a rod, which is: 1/12 * MR^2 However I need to use the...
43. ### Linear acceleration to angular acceleration

I am working on a project where i need to determine the angular acceleration from known linear acceleration. I have given it a try please let me know if its the correct approach. Linear acceleration = 70 G's (70x9.8 mts/sec2) Radius of cylinder = 0.203 mts Rotation of cylinder along center...
44. ### Simulating linear acceleration of a vehicle

Hi All, I’m new here so please forgive me if this isn’t the right section to post in. This is a bit of an epic idea/post so I’ll just start with a basic overview and see if anyone’s interested. Summary: I’m a very good software engineer and I know a reasonable amount about maths...
45. ### Connection between Tension/Torque/Inertia, & linear acceleration

Homework Statement A block with mass m = 5.00 kg slides down a surface inclined 36.9 degrees to the horizontal. The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 25.0 kg and moment of inertia...
46. ### Stepped Pulley: Angular and Linear Acceleration

A stepped pulley is essentially a system of connected cocentric disks that have different radii. A stepped pulley (I= 2.0 kg*m^2) is placed on a frictionless axle and then strings are attached to two radii of 20 and 50 cm. The other ends of the strings are attached to a 2.0 and 1.0 kg mass...
47. ### Rotational Momentum and linear acceleration

[b]1. A rigid, massless rod has three particles with equal masses attached to it as shown below. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Assume that m and d...
48. ### Getting the magnitude of linear acceleration from angular position equation

Homework Statement The angular position of an object that rotates about a fixed axis is given by \theta(t) = \vartheta e^\betat, where \beta= 2 s^−1, \theta = 1.1 rad, and t is in seconds. What is the magnitude of the total linear acceleration at t = 0 of a point on the object that is 9.2 cm...
49. ### Linear acceleration and angular acceleration

Homework Statement How do I solve for linear acceleration or angular acceleration without one or the other? I am given the mass of the object (a yoyo), the inner radius, the outer radius, and Icm (moment of inertia at the center of mass). Attached in a picture of the problem...
50. ### Linear acceleration in a uniform magnetic field due to torque

Here the extra credit question I'm stuck on: A square loop (perimeter of 4L and hinged along one side) is made of a wire that has a mass per unit length of 0.1000 kg/m and carries a current of 5.000 A. A uniform magnetic field of 10.00 mT directed perpendicular to the hinged side exists in...