# What is Radial acceleration: Definition and 85 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. ### 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...
2. ### Parabolic Pressure Distribution in a Jet

Assume the jet is straight but the radius of the jet varies over it's length (like a jet of water falling which narrows due to gravitational acceleration). Also ignore viscosity. A pressure gradient would be required to accelerate the fluid radially. Because during an expansion transformation...
3. ### Atmospheric pressure as a function of altitude

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4. ### What happens when a car turns?

A car moving at constant speed is in uniform circular motion, thus having centripetal acceleration of ##a=\frac{v^2}{R}##. The force associated with this acceleration is known to be friction. But friction, in nature, appears as an opposition to the relative motion between two surfaces whether it...
5. ### 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.
6. ### 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).
7. ### Exploring Radial Acceleration and Displacement

From what I understand, ##a_{r} = v_{tan}^2 /r## ##a_{r} = (r\omega)^2 /r## ##a_{r} = r\omega^2## ##\omega^2 = \frac{a_{r}}{r}## ##\omega^2 = \frac{2+2t}{0.12}## ##\omega = \sqrt{\frac{2+2t}{0.12}}## ##s =\int_{0}^{2} \sqrt{\frac{2+2t}{0.12}}## After integrating, I still can't seem to get the...
8. ### Why does radial acceleration act toward the center?

Acceleration of a rotating link has two components,Tangential (change in the direction) Radial (change in the magnitude). Why the direction of Radial acceleration is considered towards center (Centripetal)? what about centrifugal?
9. ### Radial Acceleration in Polar/Cylindrical Coordinates

My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ? If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...
10. ### Radial Acceleration on a string

Homework Statement A ball on the end of a string is whirled around in a horizontal circle of radius 0.250m. The plane of the circle is 1.06m above the ground. The string breaks and the ball lands 1.90m (horizontally) away from the point on the ground directly beneath the ball's location when...
11. ### Difference between radial and centripetal acceleration?

Homework Statement I'm not understanding the difference between them, this is for Uniform Circular Motion. Homework Equations ar = -ac = -v2/r The Attempt at a Solution So what i know is radial acceleration goes in a direction towards the radius (perpendicular to velocity), and tangential...
12. ### I Radial Acceleration of Rotating Singularities: Planck Length & Beyond

And if so, how much? Should the radius be thought of as zero, an infinitesimal, or as the Planck length? v2/r = ω2r If its zero, then you immediately run into a problem when trying to calculate it with linear velocity. v2/r = ar v2/0 = undefined OR ω2r = ar ω20 = 0 Which would mean that...
13. ### Radial & Tangential Acceleration of a Car at Indianapolis 500 | Physics Solution

Homework Statement A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 200 m. Determine the tangential and radial acceleration of the car when it is halfway through the arc, assuming constant tangential...
14. ### Uniform circular motion -- How can radial acceleration have a calculated value?

In uniform circular motion, direction of particle is changing at every moment but its speed remains the same. If the magnitude of velocity or speed remains the same, change in magnitude of velocity is zero. Then how come radial acceleration can have a calculated value since acceleration = change...
15. ### Finding relative error for radial acceleration

Homework Statement I'm trying to find da/a to calculate the relative possible error in the radial acceleration. The equation I have to derive from is a = 4π²n²rt ⁻² (it cannot be a = v²/r). I'm not really sure how to find da since it has 3 variables? Homework Equations a = 4π²n²rt ⁻² da/a =...
16. ### Centripetal and Tangential Acceleration

Homework Statement A car drives on a circular road with radius ##R##. The distance driven by the car is given by ##d(t) = at^3 + bt## [where ##t## in seconds will give ##d## in meters]. In terms of ##a##, ##b##, and ##R##, and when ##t = 2## seconds, find an expression for the magnitudes of (i)...
17. ### Radial acceleration of a particle in a groove on a turntable

Homework Statement A horizontal turntable rotates at a constant rate ω about a fixed vertical axis through its center O. A particle of mass m can slide in a fictionless circular groove of radius r centered at O' which is r/3 from O. What is the radial acceleration of m in direction O'm...
18. ### Finding radial & tangential acceleration at a point

Homework Statement A point on a rotating turntable 20.0cm from the center accelerates from rest to final speed of 0.700m/s in 1.75s. At t=1.25s, find the magnitude and direction of (a) the radial acceleration, (b) the tangential acceleration, (c) the total acceleration of the point. Homework...
19. ### Centripetal Force Theory Questions

Homework Statement Answer True, False, or Cannot tell to each of the five statements below. A small projectile is launched horizontally 1 m above the surface of a smooth, airless planet, with sufficient speed for orbit. A bug riding in a small hole in the projectile has apparent weight...
20. ### Angular vs Radial Acceleration

Homework Statement The cosmoclock 21 Ferris Wheel in Yokohama City, Japan, has a diameter of 100m. Its name comes from its 60 arms, each of which can function as a second hand (so it makes one revolution every 60.0s). a) Find the speed of the passengers when the Ferris wheel is rotating at...
21. ### Rotational motion - finding tangential acceleration

1. The problem A 6 kg block is released from a height of 5 m on a frictionless track and goes into a half pipe with a radius of 2 m. Determine the tangential and radial components of the acceleration when the block reaches a height of 2 m.Homework Equations Ac= v^2/r. At = r*angular...
22. ### Radial acceleration in a pendulum

I'm just trying to think how I would expect radial acceleration to look like in a pendulum. I would expect a sine wave of sorts but instead of oscillating around zero I would expect it to be around a positive number as this acceleration is always in the same direction. Also if I was to compare...
23. ### Determine the magnitude of its radial acceleration for ball

< Mentor Note -- Thread moved from the General Physics forum to HH > A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9 degrees past the lowest point on its way up, its total acceleration is (-22.5i + 20.2j) m/s^2. For that instant, (a)...
24. ### Circular Motion with time-dependent radial acceleration

Homework Statement A particle is traveling on a circle with a radius R. The particle's radial acceleration is given as: a_r=At^4 At time t=0 the particle is at (R,0) . A. Find the distance that the particle has traveled as a function of time S(t) . B. Display the particle's acceleration...
25. ### Total acceleration at the bottom of a rolling wheel

A tundra buggy, which is a bus fitted with oversized wheels, is stuck in Churchill, Manitoba, on slippery ice. The wheel radius is 0.84 m. The speedometer goes from 0 to 27 km/h while the buggy moves a total distance of 7.0 m in 9.0 s. Find the magnitude of the total acceleration of a point at...
26. ### Find Initial Velocity of a Bullet

This problem was given verbally during a class period, so I will set it up in my own words. A bullet (.012kg) is fired at a block (.800kg) hanging on a strong, massless string of length 1.6m. After the collision the bullet is embedded in the block. When the block is .8m above its original...
27. ### Direction of radial acceleration

I have a big confusion. There is a question in my book which basically says that a ball is tied to a string and rotated. and it asks me to tell whether the following statement is true of false. Direction of radial acceleration MAY remain the same. This statement is true. Please explain to me a...
28. ### Centripetal vs Radial acceleration

I am reading introductory physics from Serway. Where they say if a_r is radial acceleration and a_c is centripetal acceleration then a_c = v^2/r and a_r = -a_c = - v^2/r But aren't the radial and centripetal acceleration same (correct me if I am wrong)? Why is there a minus sign? The...
29. ### Find the radial acceleration

Homework Statement A wheel with a radius of 0.2 m has a constant angular acceleration of α = 3.00 rad/s^2. Find the radial acceleration. Homework Equations arad = ω^2*r ω^2 = ωo^2 + 2*α(θ - θo) → ω = √(2*α*θ) The Attempt at a Solution ω = √6 rad/s → a rad = 6*0.2 m/s^2 = 1.2...
30. ### Tangential and radial acceleration

A ball tied to the end of a string 0.50 m in length swings in a vertical circle under the influence of gravity. When the string makes an angle x= 20 degrees with the vertical, the ball has a speed of 1.5 m/s. Find the magnitude of the radial component of acceleration at this instant. So i have...
31. ### Radial acceleration in uniform circular motion

Why is there only a radial component of acceleration present if a body is undergoing uniform circular motion whereas in non uniform circular motion both tangential and radial component of acceleration are present?
32. ### When to use centripetal vs. radial acceleration

My question is more general than anything. When do I use centripetal acceleration vs. radial acceleration. The solutions in my physics book define a in polar coordinates as positive (v^2)/r. However, my professor uses -((v^2)/r). When do I know when to use each respective form? Thanks
33. ### Uniform Circular Motion Derivation of Radial Acceleration

Homework Statement I am trying to derive the formula a_r=\frac{v^2}{r} for uniform circular motion (for personal understanding, this is not an assignment). But am having some difficulty. I have seen other proofs, but I want to know why my approach is wrong. The Attempt at a Solution...
34. ### Change in magnitude of radial acceleration

Homework Statement A wheel changes its angular velocity with a constant angular acceleration while rotating about a fixed axis through its center. Show that the change in the magnitude of the radial acceleration during any time interval of a point on the wheel is twice the product of the...
35. ### Tangential and radial acceleration

Hi, I am reviewing a problem with the associated solution and there is something i don t understand. Imagine a triangle with vertices l, masses m are attached to the two end of the vertices and on the top end vertice there is a pivot so that the triangle can swing. We start with the triangle...
36. ### How would I go about computing the radial acceleration when given i and j components?

Homework Statement I attempted this problem, and i have a midterm tommorow. I thought my approach was correct but I don't have a clue if it actually is. I drew a simple right angle triangle according to the information given in the question. A ball swings in a vertical circle at the end of a...
37. ### Radial Acceleration of ball

Hi! I am reviewing for the Physics GRE and am perplexed by this problem: Homework Statement A ball swings in a vertical circle at the end of a rope 1.5m long. When the ball is 36.9 degrees past the lowest point on its way up, its total acceleration is (-22.5, 20.1)m/s^2. At this instant...
38. ### Tangential and Radial Acceleration

Homework Statement A point on a rotating turntable 20.0 cm from the center accelerates from rest to a ﬁnal speed of 0.700m/s in 1.75s. (a) At t = 1.25s, ﬁnd the magnitude and direction of the radial acceleration, (b) the tangential acceleration, and(c) the total acceleration of the point...
39. ### Tangential and radial acceleration

Hey I have an accelerated circular motion problem. I have only the position equation, from which I derived the velocity and acceleration. how can I tell what is the tangential acceleration and what is the radial acceleration? If you could point me towards a source to read about the...
40. ### Tangential acceleration - radial acceleration

Hi, I got a ball in a circualar motion on a frictionless table and in a uniform circle. I need to calculate the tangential acceleration and radial acceleration. What I know: Radius: 0.4m Tangential velocity: 0.50m/s^-1 (constant)Are theese formulas right for this problem? Radial...
41. ### I with Radial Acceleration -it is an easy one

The period of the rotation of an airplanes ellipse is T=3 milliseconds,linear speed in the top is 3*10^3 m/s.What's the centripetal(radial) acceleration of the top?I need a step by step guide it would be really helpful.Thanks.
42. ### Physics problem: Radial acceleration, forces, and work & energy problem

Homework Statement In case the numbers are hard to read: Mass of the cart- .5g Initial Velocity- 1.5 m/s The height of the first hill is 2. Radius of the circle- .09m I need to find velocity (final, i think) force(s) on the cart at point A the magnitude of the force(s) at point...
43. ### Tangential and Radial acceleration - Sin and Cos simple question

Homework Statement Im confused about something. Ill post the answer sheet to a question. It has all the data you need. BELOW: NOW... for Tangential component of the acceleration, WHY did they pick cos? and for Radial, WHY did they pick sin? I am starting to do a lot of FBD to equations...
44. ### Radial acceleration: Rotating Carousel

Homework Statement A horse located 8.0m from the central axis of a rotating carousel moves at a speed of 6.0 m/s. The horse is at a fixed height (it does not move up or down). What is the net force acting on a child seated on this horse? The child weight is 130N. Homework Equations...
45. ### Is radial acceleration and centripetal acceleration the same thing?

In uniform circular motion, Is radial acceleration and centripetal acceleration the same thing? Just a vector pointing towards the center? i.e. a synonym?
46. ### Tangential and Radial Acceleration of car around a curve

Hi, I have a problem with this problem.. The figure (in the attachment) shows a bird's-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which vector shows the direction of the car's average acceleration between these two points...
47. ### How Do You Calculate Radial Acceleration at the Equator Due to Earth's Rotation?

Knowing that the diameter of the Earth at the equator is 12 740 km, compute the radial acceleration of a point on the surface of the Earth at the equator, due to the rotation of the Earth about its axis.
48. ### A radial acceleration problem.

Homework Statement [PLAIN]http://img508.imageshack.us/img508/6861/21296472.jpg I tried to get a_rad and if i didn't make any mistake, then a_rad = 15.79 m/s. I need to find angle when the bean is at vertical equilibrium. Homework Equations a_rad= v^2/R = 4(pi)^2R/T^2...
49. ### Radial acceleration, car sircular path

Homework Statement A car is traveling with constant speed over a hill and down a hill. The radius of the curve is the same. At the top of the hill, the driver experience no normal force from the ground. The mass of the driver is 70.0kg a) calculate the value of the normalforce experienced by...
50. ### Ball in Vertical Circle on End of String, Tangential and Radial Acceleration

Homework Statement A ball swings in a vertical circle at the end of a rope 1.30 m long. When the ball is 36.1° past the lowest point on its way up, its total acceleration is (-22.5 i + 20.2 j) m/s2. (a) Determine the magnitude of its radial acceleration. (b) Determine the speed and velocity...