# Centripetal acceleration Definition and 56 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. ### Finding tension as a function of distance from the center of rotation

I'm not too sure how to account for both the mass and the rope at once. I think the following are true for the two individually: For the mass at the end, ## T = m ω^2 L ##, following from ##a = v^2/r##and ##v=ωr##. For the rope, ##dT = ω^2 r dM##, where ##dM = λ dr## and λ is the mass per unit...
2. ### Finding the angle and velocity at which a space station reaches the moon of the planet

A station is orbiting a planet at a distance R1, a moon is orbiting the planet at distance R2 with the period T. The planet itself has a radius rp and a mass mp. We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase. Determine the...
3. ### 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...
4. ### Is Gravity the only force doing work on a roller coaster cart?

Why I think gravity *is* the only force doing work on the rider: 1) The only forces acting on the rider are gravity and the normal force. Broken down into their component vectors, we have: -> The component of the force of gravity moving parallel to the rider's direction of motion -> The normal...
5. ### 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...
6. ### A small block ##m## is projected with speed ##v_0 = \sqrt{2gR}## from bottom of a fixed sphere of radius ##R##. (Vertical circular path)

Does the block move along the pink dotted lines as attached in the figure below? I tried to draw the FBD of the small block ##m ## at the lowermost point which is also attached below.(The direction of ## v_0 ## is actually tangential) Is the figure above correct? If not, why?
7. ### Force on a pin from a pendulum and a string

1. Determine the velocity of the ball when it is 30degrees from the horizontal: U1 = mgh = mg(0.8m) U2 = mgh = mg(0.4+0.4cos(30)) = mg(.74641) ΔU = U2 - U1 = mg(.74641 - .8) = mg(-0.051433) T1 =0 T2 = 0.5mv^2 ΔT = T2 - T1 = 0.5mv^2 ΔU = ΔT mg(-0.051433) = 0.5mv^2 ====> v = 1.025394 2. Use...
8. ### Angular and linear velocity question

I have a question, let’s say I’m holding a long piece of wood such as. 1’ x 6’ plank and I’m rotating it in a circle by spinning around with my hands extended, I suddenly let go, what happens to the velocity of the wood since every point on the wood that is a different distance from the center...
9. ### Questions: Spherical habitat

Consider a hollow sphere roughly the size of the moon, spun up to produce 1g of centripetal acceleration along a band at its equator (about 15000 kph) Big stuff, I know. I have a few questions about the implication of such a system, and I hope someone can help me find some answers! - How tall...
10. ### 'They' haven't considered centripetal acceleration

Homework Statement A train is moving counter-clockwise with a constant speed of 10 m/s in a circle of radius ##\frac {16} π## m. The plane of the circle lies in the x-y plane. At time t = 0, the train is at P, when a stone is thrown from it with a speed of 10 m/s relative to the train towards...
11. ### Gravitation sum related to Centripetal Acceleration

Homework Statement The distance between the centres of the Earth and the moon is 60 times the radius of the earth. Calculate the centripetal acceleration of the moon. Acceleration due to gravity on the Earth's surface is 10m/s. Homework Equations Centripetal acceleration= v^2/R Orbital...
12. ### Find the apparent weight

Homework Statement A car traveling on a straight road at 9.15m/s goes over a hump in the road. The hump may be regarded as an arc of a circle of radius 10.4m. What is the apparent weight of a 665N woman in the car as she rides over the hump? Homework Equations ##F=ma##; ##a=v^2/r## The...
13. ### Given speed/mass find R (centripetal)

Homework Statement 1) A 50kg person drives a car at 8.3m/s over a hump in the road. At the top of the hump, the driver feels a force of 143 N from the seat. What is the radius of the hump? 2) At what speed will the car need to move over the hump for the person to feel weightless at the top...
14. ### 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...
15. ### Question regarding centripetal acceleration/period

Homework Statement A satellite orbits the Earth every 6.0 hours in a circle. Radius = 70,000 km a) What is the period of rotation? b) What is the acceleration of the satellite? Homework Equations a = v2/r Fc = mv2/r v = 2pir/T The Attempt at a Solution For a, I converted 6 hours into 21600...
16. ### Relative Centripetal Acceleration

Let's say you have two rings. Both rings have the same radius and are aligned so that the holes are perfectly parallel to each other and a straight line can be drawn through them without interference. Both rings spin along the same axis with the same speed, but in opposite directions. If you...
17. ### Vertical Circles Centripetal Acceleration

Homework Statement A jet pilot takes his aircraft in a vertical loop. V is 840 km/hr (233.3 m/s) find the min. radius of the loop to that the centripetal acceleration at the bottom does not exceed 6 Gs. Homework Equations a = v^2 / r F = ma The Attempt at a Solution I don't know where to...
18. S

### Derivation of an expression for centripetal acceleration

Homework Statement I have derived the expression for the velocity of the satellite v= root of GM/r however I'm struggling to derive an expression for the centripetal acceleration of a satellite orbiting Earth. Homework Equations The Attempt at a Solution I'm not entirely sure which equations...
19. J

### Dynamics and Circular Motion Problem

Homework Statement A 2 kg tetherball swings around a vertical pole attached to two ropes each at a 30 degree angle from vertical. Each supporting rope is 1.5 meters long, and the ball travels at 8 m/s long. Homework Equations The question doesn't ask what they're looking for, so I assume they...
20. N

### Centripetal Acceleration Problem: Finding Angular Speed

Hi all, I've been lurking around the forums for a while to get help with homework but I figured I'd finally make an account to get direct feedback. I'm having problems with this centripetal acceleration problem, Homework Statement "In an old-fashioned amusement park ride, passengers stand...
21. S

### Centripetal Force

Homework Statement There is a subway derailed. Radius of an unbanked curve is 150 m. An unused strap hangs at a 15 degrees angle to the vertical just before the accident. Did the train exceed 35 km/h and what speed was it at just before the accident. Homework Equations F=ma=m(v^2/r) The...
22. K

### I Determine the force exerted by the seat on the child at the bottom of the ride

A child of mass m rides on a Ferris wheel as shown in figure (a). The child moves in a vertical circle of radius 14.5 m at a constant speed of 2.85 m/s. Determine the force exerted by the seat on the child at the bottom of the ride. Express your answer in terms of the weight of the child mg...
23. J

### Find the tension in the lower string and the rotation rate

Homework Statement A 700g ball rotates around a vertical shaft supported by two strings. If the tension in the upper string is 20.0 N, determine (I have attached the file) a. The tension in the lower string. b. The rotation rate in rpm of the system. Homework Equations [/B] F=ma F= m...
24. ### Doubt with rotating body and force

Hello. Let's image a bar. In one side is attached to a body so the bar can rotate over this axis. There is no friction between the two bodies. The system is at rest in t=0. A force acts forming a 90° angle with the bar. The bar moves and begin to rotates. The force dissapear. There is no force...
25. ### Are momentum and centripetal acceleration related somehow?

I have been wondering, simple question, really: What is the relationship between momentum and centripetal acceleration, if there is one? Is there a relationship in terms of velocity, maybe, or is there none whatsoever?
26. ### Definition of 'with the vertical' in this question?

Homework Statement (please ignore something that is not english) Homework Equations ac=v^2/r Fc is about 6.0E3 N and ac is about 5.0 m/s^2 (b) is the problem... The Attempt at a Solution what is 'with the vertical' here? the direction/opposite of ac or the direction of v?
27. ### Problem using centripital accel.... Can you check my work?

Homework Statement A student ties a 500 g rock to a 1.0-m-long string and swings it around her head in a horizontal circle. At what angular velocity in rpm does the string tilt down at a 16 degree angle? Homework Equations F = (m*v^2)/r v = r*w The Attempt at a Solution [/B] First I solved...
28. ### Ball doing a loop

Homework Statement A ball with radius ##r## is inside a hollow cylinder with radius ##r+R##. In the first part of the assignment, one has to calculate the minimum kinetic energy the ball has to have at the bottom in order to complete a full loop in the cylinder. It turns out to be...
29. ### Rubber Band Spinning in midair

Homework Statement A uniform thin circular rubber band of mass M and spring constant k has an original radius R. Now it is tossed into the air. Assume it remains circular when stabilized in air and rotates at angular speed ω about its center uniformly. Derive an expression for the new radius...
30. ### Definition of centripetal force

Homework Statement Hi, If an object is undergoing uniform circular motion, then the net force is acting perpendicular to the instantaneous velocity, and this is called the centripetal force. However, if the object is moving in a circle but the magnitude of its instantaneous velocity is not...
31. ### Centripetal acceleration

Recently, I was looking into centripetal acceleration and there's something I don't understand. According to my book, during uniform circular motion, the acceleration is a= v^2/r where v is the speed at which the object is moving and r is the radius of the circle. However, this formula is...
32. ### Implementing angular momentum approach in problem

Homework Statement An object is in uniform circular horizontal motion at the end of a chord of length L. Its tangential speed is v. The chord is pulled into length 0.5L in such a way that the tension in the chord remains constant. As a result, the tangential speed: a) remains constant b)...
33. ### Question on energy conservation with centripetal acceleratio

Homework Statement The right answer is E, and I have no idea how to solve this problem. Please advise on how to proceed. Thanks in advance. Homework Equations conservation of mechanical energy?? The Attempt at a Solution Many attempts were done, but I am lacking on theory with this. How...
34. ### Question about circular motion of planets

Homework Statement Homework Equations I know that Fc = m * centripetal acceleration, where the Fc = the force of gravity The Attempt at a Solution [/B] I was able to use process of elimination to get B for 25 correctly, but I am not able to understand how it is the right answer. How can...
35. ### Question on Orbits and Kepler/Uni. Grav. Laws

Homework Statement The picture has the problem question. OK. When the moon is at point B, the distance from the moon to the center of the planet is most nearly: A) (1/25) * rA B) (1/5) * rA C) (1/ sqrt(5) ) * rA D) rA E) sqrt(5) * rA. Homework Equations Newton's law of gravitation...
36. ### Directions of centripetal acceration and gravity on Earth?

Im picturing a stationary object at the equator of the earth, going around in uniform circular motion due to the Earth's rotation. The centripetal acceleration would point directly inwards into the Earth at all points in the circular rotation, and gravity would also point in the same direction...
37. ### Centripetal acceleration formula

Homework Statement In a certain carnival ride, visitors enter a circular room with radius r=9.1m. The room then begins spinning around its center, reaching an angular speed of 1.7rad/s. What centripetal acceleration do the riders experience? Homework Equations ac= v^2/r The Attempt at a...
38. ### 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...
39. ### Rotating platform on top of another rotating platform

Homework Statement Have platform A that is being spun by a centrifuge with a radius R1 and centripetal velocity of w1. On top of platform A is a Lazy Susan (Platform B) that spins about a radius R2 with a centripetal velocity of w2. There are accelerometers placed on the the purple platform...
40. C

### The TNB components of the jerk vector

It can be found in any advanced calculus textbook the proof that, for a "well-behaved" space curve, the acceleration vector can be decomposed into components along the tangent and normal unit vectors. The acceleration vector is always orthogonal to the binormal vector. The decomposition is...
41. ### Centripetal Force Washing Machine

I know that the centripetal force is the resultant force which points to the center. So in the case of a washing machine, what force pushes the clothes and water to the outer edge? There is not centrifugal force, but then how come all the clothes appear to get pushed to the circumference of the...
42. ### Uniform circular motion

Homework Statement i was going through uniform circular but a confusion popped out of my head . as i have read before the Rutherford atomic model was only rejected due to the fact that electrons moving in circular orbits need to accelerate constantly to maintain a uniform speed but the...
43. ### Confused abt derivation of centripetal acceleration

A comparison of corresponding parts of these two similar isosceles triangles yields velocity triangle displacement triangle where |-vo| = |vf| = v In a small time interval Δt, the arc length s → c. Okay, so I got this from Physics LAB, and I don't understand the last statement that...
44. ### Friction in non-uniform circular motion of a car

Hi guys... So i searched the net for 2 whole days and found a couple of topics on how static friction is responsible for creating the force required to keep the body moving in a circle.. Friction points towards the center of the circle ONLY when the car is free wheeling i.e moving at a constant...
45. ### Acceleration of stone caught in tire tread

1) Problem Statement: A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road, is (A) vertically upward (B) horizontally forward (C) horizontally backward (D)...
46. ### Centripetal Acceleration Outwards

Hi. I have a question that I can't seem to figure out in my self study of physics. Why does centripetal acceleration point inward? When I drive around a corner, my body experiences a push away from the corner. I go that way, however, because of the car pushing me towards it. Not because of the...
47. ### Angular motion-centrifuge problem .

Homework Statement : A centrifuge starts from rest and speeds up at 3400rpm after 50 seconds. a sample is at a distance of 37.5mm from the centre 1) find the angular acceleration 2) calculate the centripetal acceleration [/B] Homework Equations : v2 / r v = rω a = rω2 a=Λω/Λt 3. The...
48. ### Problem with Centripetal velocity on a banked corner

first of all thanks for reading and especially thank you to people who helped with my previous question here https://www.physicsforums.com/threads/does-the-coefficient-of-friction-change-with-the-angle.798572/#post-5019349 Unfortunately i am having more problems with this instructor insisting...
49. ### Proving Centripetal Acceleration Physically?

How Can I Prove this Physically Homework Statement [/B] So I need to do a project where I prove centripetal acceleration. All the cases I've seen of where it's proved is using formulas, though I need an actual project. By an actual project I mean something like...
50. ### Help with physics of flight paths?

Hi all, If anything here is incorrect or confusing or seems trivially simple, I apologize: I'm not a physicist and created an account specifically to get help on this from some people who are! My question is this: Assume a plane has a constant airspeed and you wish to fly a circular pattern...