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. R

    Centripetal Acceleration and Tangential Acceleration problem driving me crazy

    A car is tested on a 230 m diameter track. If the car speeds up at a steady 1.2 m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration? it seems simple, but i just can't seem to get it!... find: change in time when centripetal...
  2. C

    Centripetal Acceleration Space Shuttle Problem

    Homework Statement Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circles the Earth 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 accleration at the Earth's...
  3. H

    Is the Net Force at the Bottom of a Vertical Circle Greater or Lower Than MG?

    You are whirling a rubber stopper of mass something attached to a string in a vertical circle at high constant speed. At the bottom of the circle, the net force that causes acceleration is my answer was Vertically upward and greater in magnitude than MG. but the answer in the book says...
  4. P

    Finding centripetal acceleration

    1.The blade of a windshield wiper moves through an angle of 90 degrees in .28 . The tip of the blade moves on the arc of a circle that has a radius .76m. What is the magnitude of the centripetal acceleration at the tip of the blade. 2. Ac= v^2/r 3. okay, the accleration should...
  5. C

    Conservation of mechanical energy, centripetal acceleration, independence question

    Show that a roller coaster with a circular vertical loop. The difference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g's-that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this...
  6. C

    Conservation of Mechanical Energy and Centripetal Acceleration Problem

    Show that a roller coaster with a circular vertical loop. The difference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g's-that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this...
  7. V

    Calculating Maximum Speed and Acceleration for an Amusement Park Ride

    Homework Statement An amusement park ride carries riders in a horizontal circle with radius 5m. 1) If the centripetal acc. is limited to .4 g for safety, what is the max tangential speed? 2) If the tangential speed is doubled, what is the new acceleration? Homework Equations A=...
  8. G

    What is the Required Centripetal Acceleration for a Stone to Reach 25 Meters?

    Homework Statement You plan to throw stones by using a sling of length 1.3 m which you whirl over your head. Suppose you wish to throw a stone a distance of 25 m. What must be the centripetal acceleration of the stone just before its release if it is to reach this distance? Assume that the...
  9. F

    Exploring Coriolis vs Centripetal Acceleration

    according to the figure attached below , do we have a coriolis acceleration on the slider and why ? why can't we say that it is a centripital acceleration ? I want to know the difference between coriolis accelration and centrepetal acceleration , cause As I know , coriollis...
  10. A

    Slight confusion about centripetal acceleration

    I just read in my book that the farther you are from the axis of rotation the greater the centripetal acceleration. But when dealing with circular motion the centripetal acceleration decreases as you increase the radius. Am I missing something? Or did I just confuse 2 different things? Thanks...
  11. Z

    Speed boat question: calculating centripetal acceleration

    1.Speedboat A speedboat with a length of 10.2m and a mass of 247 kg is negotiaging a circular turn (radius = 33 m) around a buoy. During the turn, the engine causes a net tangential force of magnitude 521 N to be applied to the boat. The intial speed of the boat going into the turn is 4 m/sec...
  12. A

    Tangential and Centripetal Acceleration

    Again, I was having trouble with something that I think I resolved, but I still lack the confidence in these problems, so I am asking people to check my solution. Homework Statement A pendulum of mass M with a massless string length L is released from the horizontal. Theta initial is 90...
  13. T

    Centripetal Acceleration in Terms of g?

    Homework Statement Calculate the magnitude of the centripetal acceleration at 8.4 cm from the centre of the centrifuge when it is spinning at 6.0x10^4 rpm. Express your answer in terms of g (acceleration due to Earth's gravity.) Homework Equations Ac = v^2 / r The Attempt at a...
  14. T

    How Do You Calculate Centripetal Acceleration in Terms of g?

    Homework Statement Calculate the magnitude of the centripetal acceleration at 8.4 cm from the centre of the centrifuge when it is spinning at 6.0x10^4 rpm. Express your answer in terms of g (acceleration due to Earth's gravity.) Homework Equations Ac = v^2 / r The Attempt at a...
  15. B

    What Speed Keeps Theme Park Ride Cars on Track?

    the cars on a theme park ride each have a mass of 500Kg and travel round a verticle loop of diameter 20m i need to know the minimum speed at which the carts are traveling in order to remain in contact with the loop as they go round. and the maximum reaction of the track
  16. B

    Centripetal acceleration and force

    The cars on a theme park ride each have a mass of 500 kg and travel around a vertical loop of diameter 20m. What is the minimum speed at which the cars must enter the loop in order to remain in contact with the track and What will then be the maximum reaction of the track? M=mass g=gravity...
  17. B

    Centripetal Acceleration Part II

    [SOLVED] Centripetal Acceleration Part II Homework Statement (From previous question) In order for a satellite to move in a stable circular orbit of radius 6689 km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius of the orbit...
  18. B

    What Is the Correct Calculation for Satellite Speed in a Stable Orbit?

    [SOLVED] Centripetal Acceleration Homework Statement In order for a satellite to move in a stable circular orbit of radius 6689 km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius of the orbit. What is the speed of the...
  19. J

    Centripetal acceleration and coefficient of 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 0.3, how far from the center of the record can the coin be placed without having it slip off? Homework Equations a=v^2/r The Attempt...
  20. M

    Centripetal acceleration centrifuge problem

    [SOLVED] centripetal acceleration problem Homework Statement Find the centripetal acceleration at the top of a test tube in a centrifuge, given that the top is 5.0 cm from the axis of rotation and that its linear speed is 76 m/s.Homework Equations Ac = v^2/r The Attempt at a Solution So...
  21. T

    Vertical Circular Motion & Centripetal Acceleration

    [SOLVED] Vertical Circular Motion & Centripetal Acceleration Homework Statement 1) A car travels at a constant speed around a circular track whose radius is 2.1 km. The car goes once around the track in 410 s. What is the magnitude of the centripetal acceleration of the car? Homework...
  22. C

    What is the Centripetal Acceleration of a Race Car on a Circular Track?

    Homework Statement I am having difficulty with a problem: A race care goes around a level, circular track with a diameter of 1.00 km at a constant speed of 90.0 km/h. Wha tis the car<s centripetal acceleration in m/s^2? Homework Equations Ac=v^2/r The Attempt at a Solution I'm...
  23. B

    Centripetal acceleration of Earth around Sun

    Problem: The Earth's orbit (assumed circular) around the sun is 1.5e11 m in radius, and it makes this orbit once a year. What is the centripetal acceleration of the earth? Equations: a = (v^2) / r T = (2*pi*r) / v My work: T = (2*pi*r) / v; 1 year = (365 days / 1 year)*(24 hours /...
  24. A

    Centripetal Acceleration Question

    Is it possible to drive your car so as to have a nonzero centripetal acceleration while your tangential acceleration is zero?
  25. P

    Centripetal Acceleration, etc.

    [SOLVED] Centripetal Acceleration, etc. Homework Statement A space station is being built for astronauts to begin training for colonizing other planets. The rate of rotation is chosen so that the outer ring (r=2150m) simulates the acceleration of gravity on the surface of Venus (8.62m/s^2)...
  26. I

    Need help with centripetal acceleration problem.

    PROBLEM A biophysicist wants to separate sub-cellular particles with an analytic ultracentrifuge. The biophysicist must determine the magnitude of the centripetal acceleration provided by the centrifuge at various speeds and radii. Calculate the magnitude of the centripetal acceleration at...
  27. S

    What is the correct formula for calculating centripetal acceleration?

    What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is moving 7.0m/s? I thought the formula was v^2/r =ac But when I do that i get 1.4m/s^2 and it is not the right answer. Can someone tell me what I'm doing wrong, or if I've...
  28. S

    Centripetal Acceleration in Satellites Question

    Homework Statement What provides the force that causes the centripetal acceleration of a satellite in orbit? 2. The attempt at a solution I'm really confused about the answer to this question because in class my teacher only taught us how to solve satellite problems if we are given...
  29. S

    Centripetal Acceleration Problem HELP

    I don't know what I'm doing wrong on this one... What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70cm when the bike is moving 7.0m/s. isn't centripetal acceleration just v^2 / r? I get 140m/s^2, but the answer is 180m/s^2
  30. P

    What Frequency Causes the Box to Slide on a Rotating Platform?

    Homework Statement A box rests at a point 2.0m from the axis of a horizontal circular platform. The coefficient of static friction between box and platform is 0.25. As the rate of rotation of the platform is slowly increased from zero, at what frequency will the box first slide...
  31. A

    Max Velocity for a Car over a Speed Bump in Uniform Circular Motion

    I'm doing problems modeling particles in uniform circular motion and one is about a car going over a speed bump. I figured out the problem, but then it asks "What is the max speed the car can have as it passes this highest point without losing contact with the road?" I'm not sure what this...
  32. S

    Please explain centripetal acceleration?

    can some1 please explain centripical accleration? i don't get it at all
  33. S

    Measuring Centripetal Acceleration Geometrically

    Is there a way to measure centripetal acceleration independent of a force measurement? If I had just a ruler, and a ball was rolling along a circular path, could I 'measure' the centripetal acceleration itself, without resorting to finding the radius, period, etc. Someone once told me that this...
  34. K

    Question about centripetal acceleration

    Homework Statement A centripetal-acceleration addict rides in uniform circular motion with period T = 6.12 s and radius r = 3.00 m. At one instant his acceleration is a = (1.00 m/s2) i + (-3.00 m/s2) j. At that instant, what are the following values? v.a and r x a Homework Equations T...
  35. C

    Centripetal Acceleration of washer spin cycle

    Homework Statement On your first day at work for an appliance manufacturer, you are told to figure out what to do to the period of rotation during a washer spin cycle to triple the centripetal acceleration. You impress your boss by answering immediately. Express your answer in terms of T...
  36. S

    Centripetal Acceleration of bicyclist

    Homework Statement A bicyclist travels in a circle of radius 25.0m at a constant speed of 9.00 m/s. The bicycle-rider mass is 85.0 kg. Calculate the magnitudes of a) the force of friction on the bicycle from the road and b) the net force on the bicycle from the road. Homework Equations...
  37. H

    Centripetal Acceleration and period of rotation

    Homework Statement In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 7.7m. What must the period of rotation be so that the centripetal acceleration has a magnitude of 3.7g ? What must the period of rotation be so that the centripetal acceleration has a...
  38. S

    Centripetal Acceleration of Earth

    Homework Statement (a) What is the magnitude of the centripetal acceleration of an object on Earth's equator owing to the rotation of Earth? (b) What would the period of rotation of Earth (in minutes) have to be for objects on the equator to have a centripetal acceleration with a magnitude of...
  39. N

    Centripetal Acceleration and velocity

    A ball on the end of a string is whirled around in a horizontal circle of radius .487 m. The plane of the circle is 1.06 m above the ground. The string breaks and the ball lands 2.26 m away from the point on the ground directly beneath the ball's location when the string breaks. The...
  40. T

    CD spinning - Centripetal Acceleration

    Homework Statement A computer is reading data from a rotating CD-ROM. At a point that is 0.0244 m from the center of the disk, the centripetal acceleration is 283 m/s2. What is the centripetal acceleration at a point that is 0.0856 m from the center of the disc? Homework Equations Ac =...
  41. B

    Centripetal acceleration of ball and rope

    Homework Statement An athlete swings a 5 kg ball horizontally on the end of a rope. the ball moves in a circle of a radius .800m at an angular speed of .500rev/second. if the maximum tension the rope can withstand before breaking is 100N, what is the maximum tangential speed the ball can...
  42. C

    Centripetal acceleration problem (very easy)

    A 2.5 kg object moves at a constant speed of 8.0 m/s in a 5.0 m radius circle. What is the object's acceleration? I'm quite sure the answer to the problem is 32 m/s^2, but apparently the right answer is 13 m/s^2. Unless I'm missing a detail about the "constant velocity" part of the problem...
  43. R

    Centripetal Acceleration of curved exit ramp

    Centripetal Acceleration ! Homework Statement An Engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the force causing the centripetal...
  44. E

    Solving a Horizontal Arc HW Problem: Centripetal Acceleration

    Homework Statement A hawk flies in a horizontal arc of radius 13.5 m with a speed of 3.9 m/s. What is its centripetal acceleration? (I correctly found this to be 1.1267 m/s².) Next question is: If it continues to fly along the same horizontal arc but increases its speed at a rate of...
  45. C

    What is the centripetal acceleration of the Earth in its orbit around the Sun?

    Homework Statement Calculate the centripetal acceleration, in units of m/s2, of the Earth in its orbit around the Sun. Assume that the Earth's orbit is a circle of radius 148,022 thousand km. Homework Equations v= 2 pi r/ T Ac = V^2/ r The Attempt at a Solution I solve for V and...
  46. B

    Centripetal acceleration and angles

    Homework Statement A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 34 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 120 m), the block swings toward the outside of the...
  47. H

    What is the centripetal acceleration of the end of the rod?

    Here is the homework question... According to the Guinness Book of World Records, the highest rotary speed ever attained was 2010m/s(4500mph). The rotating rod was 15.3cm(6in.) long. Assume the speed quoted is that of the end of the rod. What is the centripetal acceleration of the end of the...
  48. F

    Centripetal Acceleration of object orbiting earth

    Homework Statement An object orbits the Earth at a constant speed in a circle of radius 6.38x10^6m, very close to but not touching the Earth's surface. What is its centripetal acceleraion? Homework Equations The Attempt at a Solution Quick question, when would GM/r^2 equal to the...
  49. H

    A question on centripetal acceleration

    Estimate the time it takes a satellite in “near-earth” orbit to go once around the earth. To do this, assume that it is close enough to the earth’s surface that the gravitational force acting on it is about equal to its weight on earth, mg. Proceed as follows: a. Find the centripetal...
  50. F

    Centripetal acceleration of a wheel

    Homework Statement A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel’s rim? A) 1.0 m/s2 B) 4.0 m/s2 C) 0.50 m/s2 D) 2.0 m/s2 Homework Equations Would it be v^2/r? The Attempt at a...
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