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. 3

    Centripetal acceleration and velocity derivation

    in physics, I've been taught that centripetal acceleration is given by v^2/r, but when i try to derive it myself, i get a=2v^2/(pi*r). i said that if the time period is T, after a time of T/4, the velocity would be going in the next direction, i said west to south, and this gives the equation...
  2. T

    Ferris wheel problem - vertical circles and centripetal acceleration

    Homework Statement Given a Ferris wheel that rotates 5 times each minute and has a diameter of 19 m, with the acceleration of gravity as 9.8 m/s^2, what is the centripetal acceleration of a rider? Answer in units of m/s^2. (There's a diagram that shows a ferris wheel with radius 9.5 m spinning...
  3. P

    Centripetal acceleration question confirmation please

    Homework Statement what is the magnitude and direction of the centripetal acceleration necessary to confine the motion of a 0.5kg mass moving at speed 0.1m/s to a circular path 0.2m in radius Homework Equations a = v^2/r The Attempt at a Solution 0.1^2/0.2 = a a =...
  4. P

    Uniform centripetal acceleration

    Homework Statement A small ball with a mass of 3.0kg revolves uniformly in a circle on a frictionless horizontal surface. The ball is attached to a string of 1.40m to a pin set at center of circle. The object makes 2rev/sec. a)find the centripetal accel b)find the tension exerted on the...
  5. L

    Centripetal acceleration of electron

    Homework Statement In the Bohr model of the hydrogen atom, the electron revolves around the nucleus. If the radious of the orbit is 5.3x10^-11 m and the electron makes 6.6^13 r/s find a)the acceleration of the electron and b)the centripetal force acting on the electron. (this force is due...
  6. Q

    Centripetal Acceleration derivation help

    w=2π /T v=rw=2πr/T a=rw2=r(4π2r2/T) This I know, but why can't I just differentiate v with respect to t to get a? (But the answer is wrong) Can anyone tell me why? Thanks.
  7. M

    Centripetal Acceleration Problem

    Homework Statement A 1000 kg car is traveling along a flat section of the highway at a speed of 90.0 km/h. The driver notices a curve in the road ahead, with a radius of 150 m. a) If the pavement is dry and the coefficient of friction between the car tires and the road is 0.820, determine...
  8. A

    Find the centripetal acceleration of the space shuttle

    1. Suppose a space shuttle is in orbit 400 km from the Earth's surface, and circles the eart about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth's surface. 2...
  9. R

    Centripetal Acceleration of laundry dryer

    Homework Statement Hi I have a question that involves a laundry dryer, and it must turn at a certain velocity to so that when the object hits 68 degrees to the horizontal it will fall. the radius is the only given r = .330m Homework Equations the answer is stated as Fc = N +...
  10. R

    Centripetal acceleration geometry

    This is probably a geometry question more that a physics question. I am trying to prove that in uniform circular motion \Delta V/V= s/R. I am basically trying to show that S forms a right triangle with \DeltaV, when V{1} is added to V{2} as a vector. (This is to demonstrate that the triangles...
  11. D

    What Is the Maximum Speed a Car Can Maintain in a Curve Without Skidding?

    A car rounds a corner of radius r= 45 m. If the coefficient of static friction between the car and the road is= 0.82, what is the greatest speed the car can have in the corner without skidding? am i in the right direction with v^2=.82*9.8*45m? then square root both sides for the answer?
  12. R

    Tangential and centripetal acceleration problem

    A windmill starts from rest and rotates with a constant angular acceleration of 0.25 rad/s2. How many seconds after starting will the magnitude of the tangential acceleration of the tip of a blade equal the magnitude of the centripetal acceleration at the same point? I don't exactly know...
  13. D

    Centripetal Acceleration question

    Homework Statement Consider a conical pendulum that consists of a bob on one end of a string of negligible mass with the other end of the string attached to a point on the ceiling, as shown. Given the proper push, this pendulum can swing in a circle at a given angle, maintaining the same...
  14. D

    Couple Multiple Choice questions on force and centripetal acceleration.

    #1) A child ties a .25kg rock to the end of a string and whirls it at a constant speed in a horizontal circle of radius 75 cm. What, approximately, is the maximum speed at which the stone may be whirled if the string will break for a tension exceeding 300N? A. 10 m/s B. 13 m/s C. 15...
  15. V

    Problem on centripetal acceleration and friction

    Suppose a nickel sits on a flat turntable that spins at 78 rpm (revolutions per minute) while sitting on a horizontal surface. The nickel is 15 cm from the center of the turntable. What is the minimum coefficient of friction that keeps the nickel on the turntable? Relevant equations: I am...
  16. T

    Centripetal acceleration and forces - Lab help wanted?

    Homework Statement This will be kind of long because it's not just a simple problem, it's a lab. Sorry about that. So the lab is testing the concepts of forces and centripetal force, for starters. We are supposed to be "investigating the relationship between period and acceleration." In class...
  17. P

    Calculating Centripetal Acceleration & Force in Two Cars

    Two cars are traveling at the same speed of 28 m/s on a curve that has a radius of 124 m. Car A has a mass of 1080 kg, and car B has a mass of 1500 kg. Find (a) the magnitude of the centripetal acceleration and (b) the magnitude of the centripetal force for Car A, (c) the magnitude of the...
  18. P

    Centripetal acceleration centrifuge

    A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the...
  19. E

    Tension of two strings with centripetal acceleration?

    1. Homework Statement : A 4.00 kg object is attached to a vertical rod by two strings (as below). The object rotates in a horizontal circle at constant speed 6.00 m/s. mass = 4.00 kg V = 6.00 m/s Homework Equations centripetal acceleration = Ac Ac = V^2/r...
  20. C

    Centripetal Acceleration - Two people situated at different latitudes on Earth

    For starters, I feel sorry for those who have to sift through all these questions and answer them. It seems like you've got a very busy job! Hopefully there are many of you to share the workload. This is an assignment question that I get 3 attempts on. I've made two, both were incorrect...
  21. Z

    Derivation of Moment of Inertia: Why is centripetal acceleration ignored?

    Moment of inertia, I is the resistance of an object to rotational motion. It is the rotational analogue of mass and is given by the following integral, I = \intmiri2 . A simple derivation was explained to me as follows. A moment, τ is the product of force, F and lever arm, r. τ = F*r...
  22. L

    Centripetal Acceleration of pulsar

    Homework Statement Pulsars are neutron stars that emit X rays and other radiation in such a way that we on Earth receive pulses of radiation from pulsars at regular intervals equal to the period that they rotate. A certain pulsar has a period currently of length 33.085m/s and is estimated to...
  23. F

    Centripetal acceleration and airplane lift

    Homework Statement An airplane is flying in a horizontal circle at a speed of 460 km/h (Fig. 6-42). If its wings are tilted at angle θ = 37° to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an...
  24. D

    Centripetal Acceleration and Finding an Angle

    Homework Statement An old streetcar rounds a flat corner of radius 9.1 m, at 16 km/h. What angle with the vertical will be made by the loosely hanging hand straps? Homework Equations The equations I know: acceleration = velocity squared / radius (a = v^2 / R) Force = mass *...
  25. P

    Centripetal Acceleration check my reasoning

    Homework Statement ok well then... we did a lab were you have a hanging mass attached to a stirng that went through a straw and was attached to a rubber stopper. The lab was to find the mass of the rubber stopper once you know the velocity. So I was woundering if this looks correct...
  26. P

    Confused About Calculating Period in Circular Motion?

    EDIT: I figured out what I did wrong. T=\frac{2{\pi}r}{v}, not \frac{2{\pi}r}{\omega}. Now it all falls together.Homework Statement A small disk of mass m_1 on a frictionless table is attached to one end of a string. The string passes through a hole in the table and an attached narrow, vertical...
  27. Y

    How Do You Calculate Radial Acceleration and Velocity in Circular Motion?

    Homework Statement A ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is (-22.5i, 20.2j) m/s2. At that instant, (a) determine the magnitude of its radial acceleration, and (b) determine the...
  28. S

    How Does Halving the Radius Affect the Period in Centripetal Acceleration?

    What happens to the period when you cut the radius in half for a centripetal acceleration problem? a=V^2/r T=2pi*r/v I need some background on this question. I believe the answer is the period is decreased by a factor of 2. I am just slightly confused.
  29. S

    Centripetal Acceleration circular disk

    Homework Statement A circular disk of radius 30 cm is rotating with an angular acceleration of 1 radian/ s2. What is the tangential acceleration of a point on the rim of the disk? What is its centripetal acceleration if the angular speed is 3 rev / s? Homework Equations tangential...
  30. O

    G-Forces on a Rollercoaster Ride: Exploring Centripetal Acceleration

    Homework Statement A rollercoaster car is going over a hill, with a person sitting with -no- restraints. The velocity of the car and radius of the hill are such that the centripetal acceleration of the cart is 15 m/s^2. What is the relative g environment (for the rider) and how many g's does...
  31. T

    Calculating Centripetal Acceleration and Gravitational Force in a Hydrogen Atom

    Homework Statement The mass of an electron is 9 x 10-31 kg. The mass of a proton is 1.7 x 10-27 kg. The proton and electron are about 1.0 x 10-10 m apart in a hydrogen atom. What force of gravitation exists between the proton and the electron of a hydrogen atom? What is the centripetal...
  32. P

    Deriving Centripetal Acceleration

    Hi. I'm trying to derive a = (v^2)/r from the position of a particle moving in a circle. Since the equation for a particle moving in a circle is x(t) = r(isin(wt) + jcos(wt)) where w is constant. I took two derivatives to find it's acceleration. I got a(t) = -rw^2(icos(wt)+jsin(wt)). Now I'm...
  33. E

    Windsurfer making a turn (Centripetal Acceleration)

    "A windsurfer and their board have a total mass of 100 kg. While making a turn downwind, their heading changes from due west to due south over a 5 s time interval. If they maintain a constant speed of 10 m/s while doing this, determine their acceleration while taking the turn." v=Δx/Δt...
  34. E

    Centripetal Acceleration of space shuttle

    Homework Statement "The Space shuttle is located in a low orbit at a distance of 1.6 x 10^5 m above the surface of the earth. If gravity is the only force acting on the shuttle, what is the shuttle's speed while in this orbit?" Variables: Shuttle Velocity = ? r = 1.6e5 + 6.38e6...
  35. E

    Centripetal Acceleration lab question

    [b]1. This is more of a general question about a lab report I'm doing: The purpose of this lab is to find if the acceleration of a person sitting on the end of a steel beam is moving at a constant acceleration, if they aren’t accelerating, or if acceleration changes with time. I have all my...
  36. T

    Centripetal Acceleration of Stone Problem

    Homework Statement A stone at the end of a sling is whirled in a vertical circle of radius 1.20 m at a constant speed v0 = 1.50 m/s. The center of the sling is 1.50 m above the ground. What is the range of the stone if it is released when the sling is inclined at 30 degrees with the...
  37. M

    What is the Centripetal Acceleration of Earth's Orbit Around the Sun?

    Homework Statement Observing an orbit of Earth around the sun, calculate the centripetal acceleration of Earth. Homework Equations Fc = mv^2/R Only the distance aka radius was provided, to be 1.496x10^11m. The Attempt at a Solution No mass of Earth provided.
  38. L

    Centripetal Acceleration

    Homework Statement What would Earth's rotation period have to be for objects on the equator to have a centripetal acceleration equal to 9.8 m/s^2? ____ min Homework Equations Centripetal acceleration is equal to velocity * (2PI/T), where T is the period in seconds. The...
  39. U

    Centripetal Acceleration of hard drive

    Homework Statement A computer is reading data from a rotating CD-ROM. At a point that is 0.030 m from the center of the disc, the centripetal acceleration is 120 m/s2. What is the centripetal acceleration at a point that is 0.050 m from the center of the disc? Homework Equations ac =...
  40. A

    What is the speed of the roller coaster at the bottom of the dip?

    A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to three times her weight as she goes through the dip. If r = 22.0 m, how fast is the roller coaster traveling at the...
  41. S

    Centripetal acceleration and static friction

    Homework Statement A coin is placed on a record that is rotating at 33.3 rpm. If the coefficient of static friction between the coin and the record is 0.2, how far from the center of the record can the coin be placed without having it slip off? Homework Equations mv^2/r = mg(mu)...
  42. B

    Please help circular motion/ centripetal acceleration and more

    Homework Statement Ok, I am a straight A student in math so you think Physics would be easy right? Not exactly. I really need someone to explain this stuff to me. Its probably really easy if it was explained to me correctly but my teacher is not the best when it comes to breaking things...
  43. J

    Centripetal acceleration equation

    I find the equation for centripetal acceleration non-intuititive. V^2/r tells me velocity is multiplied by the velocity ( which at this stage is usually a very large number) then this is divided by the radius.. Leaves me with subdivisions that happen to equal the rate of acceleration..Dubious...
  44. M

    Total centripetal acceleration ringworld

    Homework Statement A) In Larry Niven’s science fiction novel Ringworld, a ring of material or radius 1.54 × 1011 m rotates about a star with a rotational speed of 1.4 × 106 m/s. The inhabitants of this ring world experience a normal contact force ~n. Acting alone, this normal force would...
  45. E

    Centripetal acceleration of protons in an accelerator

    Homework Statement In a certain accelerator, protons of kinetic energy 1.6 x 10^-7 J move round a circular path of diameter 2000m . Calculate: (a) the centripetal acceleration (b) the mass ans for a is 9x10^13 ms-2, for b is 1.78 x 10^-24 kg Homework Equations centripetal...
  46. R

    Calculating centripetal acceleration

    A ball of mass m is suspended from a rope of length R. The ball is set into freely swinging circular motion in a vertical plane. The centripetal acceleration of the ball at the top of the circle is 13g. The centripetal acceleration of the ball at the bottom of the circle is closest to: A...
  47. B

    Tangential and Centripetal Acceleration

    Hi, I basically just have a concept question, if the tangential acceleration of an object is zero, can at the same time its centripetal acceleration be nonzero?
  48. H

    Centripetal acceleration automobile problem

    Homework Statement 6. A car of mass 1750 kg rounds a circular turn of radius of 21 m. The road is flat and the coefficient of kinetic friction between the tires and the road is 0.3, while the coefficient of static friction is 0.76. How fast can the car go without skidding? Homework...
  49. L

    Centripetal Acceleration of North Pole

    Homework Statement Consider the radius of the Earth to be 6.38×106 m. What is the magnitude of the centripetal acceleration experienced by a person (a) at the equator and (b) at the North Pole due to the Earth's rotation? Homework Equations a = V^2 / r The Attempt at a Solution I...
  50. P

    Centripetal acceleration question

    Homework Statement Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.800 m at the rate of 6.00 rev/s. If he increased the length to 1.100 m, he could revolve the sling only 4.00 times per second. (a) What is the...
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