# What is Centripetal acceleration: Definition and 411 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. ### Centripetal Acceleration while Swinging a Stone on a String

So my initial understanding is that it completes 5 revolutions per second. I converted the 5 rev to radians, so each revolution is 2pi. Now since I got angle of rotation I can plug it into the angular velocity formula which is Angular velocity= angle of rotation/ time. However since I don't have...
2. ### Centripetal acceleration and tangential velocity of an object that revolves and rotates

Right picture is two turn tables on of top of the other, smaller turn table is connected with shaft to bigger one so it rotate around itself and in same time "revolve" around center of bigger one which is also rotate about itself. They both rotate clockwise. I observe case from inertial frame...
3. ### Circular Motion: Tangential and Normal Acceleration

Hello Physicsforum! This is my attempt: First I realised: ##a_s=a_n## Secondly I used since previus known formulas: ##a_n=\frac {v^2} {R}## ##v=v_0+a_s*t## Although now I do not know how to continue, any suggestions would be appriciated! Thanks for your help on beforehand :smile:
4. ### 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...
5. ### Roller coaster and centripetal acceleration

See attached image. The solution to this problem calculates v2 at the top of the roller coaster ride. Why is that? Shouldn't you calculate v2 at the bottom of the roller coaster ride as you require the maximum velocity there to get around the loop?
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7. ### Calculating Angle & Speed to Reach Planet's Moon from Station Orbit

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...
8. ### I The centripetal acceleration of the planets in our solar system

Relevant formulae:- Angular velocity in uniform circular motion ##=## ##\omega## ##=## ##\frac {2\pi} t##, where ##t## is the time taken to complete one revolution. Centripetal acceleration in uniform circular motion ##=## ##a## ##=## ##\omega^2r##, where ##r## is the radius of the circular...
9. ### Centripetal acceleration along a latitude of Earth

Hello, I am attempting to correctly solve this problem, however I end up with an equation that is slightly different as the one provided in the textbook solution. For question (a) I get the same thing, just instead of cos, I have cos^2 and I can't figure out where I went wrong. My process was...
10. ### Centripetal Acceleration grade 12 (forces on a bird pulling out of a dive)

How come the solution requires you to do mv^2/4 when the formula is just v^2 /r?
11. ### 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...
12. ### 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...
13. ### MHB Centripetal acceleration of viking ship in the amusement park.

Hi, Riders in an amusement park ride shaped like a Viking ship hung from a large pivot are rotated back and forth like a rigid pendulum. Sometime near the middle of the ride, the ship is momentarily motionless at the top of its circular arc. The ship then swings down under the influence of...
14. ### MHB Question about centripetal acceleration.

Hi, A mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path. The swing is suspended 2.00 m above the child’s center of mass. (a) What is the magnitude of the centripetal acceleration of the child at the low point? (b) What is the magnitude of...
15. ### Three conceptual questions on centripetal acceleration in a cone

Given such a diagram as shown above, we know that the normal force must be mg/sintheta. How is this normal force greater than the gravitational force conceptually? Is it due to the horizontal traveling (which must have been started by someone exerting a force?) compressing the sides of the cone...
16. ### 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...
17. ### 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. ### 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. ### In circular motion - centripetal acceleration is never there

So far what we know about the circular motion is that an object moving in a circle experiences a force towards the center of the circle and as a result accelerates towards this center. But we also know that an object always moves in the direction of resultant force - if two tractors moving at...
20. ### Calculate the centripetal acceleration of the car

I tried this problem 3 times. I only have two attempts left. First time: Centripetal acceleration: 7560 m/s^2 Centripetal Force: 4.7 Newtons Second time: Centripetal acceleration: 25.032 Centripetal Force: 4.7 Third Time: Centripetal...
21. ### Does the block move along the pink dotted lines

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?
22. ### 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...
23. ### Tangential acceleration and centripetal acceleration

a disc or radius r = 16cm starts spinning from rest with a uniform angular acceleration of 8.0 rad/s^2. at what time is its tangential acceleration twice the centripetal acceleration. i figured out the tangential acceleration is: Atan = α/R = 8 / .16 = 50 m/s^2 and the centripetal...
24. ### Requesting help with centripetal acceleration homework

Homework Statement A hockey puck of mass m = 80 g is attached to a string that passes through a hole in the center of a table, as shown in the figure below. The hockey puck moves in a circle of radius r = 1.10 m. Tied to the other end of the string, and hanging vertically beneath the table, is...
25. ### The change in magnitude of centripetal acceleration

When an object (e.g. racecar) moves around in circles with constant tangential velocity, constant centripetal acceleration is present. What happens to the centripetal acceleration when the racecar is at rest, then increases its speed? I know that the tangential velocity increases due to the...
26. ### 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...
27. ### How Do You Calculate Centripetal Acceleration in a Blood Centrifuge?

Homework Statement A centrifuge is a laboratory device used for spinning samples of material. In a blood centrifuge, a test tube is inserted at an angle θ=32.0° with respect to the vertical and the whole sample is spun at high speed. For a typical test that is l= 15.9 cm long and is spun in...
28. ### 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...
29. ### '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...
30. ### 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...
31. ### Uniform Circular Motion and Centripetal Acceleration (non-intuitive)

I'm in the chapter of Uniform Circular Motion and I have a hard time understating centipetal acceleration. Until now I knew that acceleration describes "how fast velocity changes in magnitude" except projectile motion because when it reaches maximum height then g is going to change the direction...
32. ### Centripetal Acceleration of Satellite

Homework Statement Hi, I am stuck on this question: A satellite of mass 1200 kg is in orbit around the Earth at a distance of 22000 km from the centre of the Earth. Calculate the magnitude of the centripetal acceleration of the satellite at this distance. The Attempt at a Solution I did...
33. ### What is the apparent weight of a woman riding over a hump in a car?

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...
34. ### 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...
35. ### 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...
36. ### Centripetal acceleration problem

Homework Statement Hydroelectric power station's turbine has a diameter of 7.5m, and a rotation frequency of 94 rotations per minute. What is the turbine's blades acceleration? P.S. This is translated from another language Homework Equations a=4π2Rn2 Where n=rotational frequencyThe Attempt at...
37. ### 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...
38. ### 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...
39. ### 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...
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### 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 EquationsThe Attempt at a Solution I'm not entirely sure which equations to...
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### 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...
42. 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...
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### Calculating Train Speed Using Centripetal Force | 15° Angle, 150m Radius

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 Attempt...
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### 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...
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### How does the kinetic energy of a swinging ball change with respect to height?

Homework Statement Imagine a ball on a string that we swing vertically so that the hight changes. By conservation of energy the velocity of the ball must change right? Because at the highest point of the swing it will have maximum GPE but at the bottom, minimum right? Watching many videos has...
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### 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...
47. ### 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...