What is Circular motion: Definition and 1000 Discussions

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same.
Examples of circular motion include: an artificial satellite orbiting the Earth at a constant height, a ceiling fan's blades rotating around a hub, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.
Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation. Without this acceleration, the object would move in a straight line, according to Newton's laws of motion.

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  1. N

    Circular Motion Regarding Car Sliding on a Curve

    Homework Statement What is the maximum speed at which a car can negotiate a level curve of 100m without sliding if the coefficient of static friction is .70? Homework Equations Ffr≤ coefficient of frictionFn F=ma Fc=mv2/r Cir.=2pir I know there are a couple more, but I'm not sure...
  2. F

    Using energy to solve circular motion problems

    Homework Statement http://img251.imageshack.us/img251/1764/66016056.jpg Solutions [PLAIN][PLAIN]http://img213.imageshack.us/img213/6821/99132292.jpg The Attempt at a Solution Now here is my question, why exactly can we not approach this problem using Energy to part a) by...
  3. Y

    Uniform Circular Motion and Water Falling From A Bucket

    1. A 2kg bucket of water is attached to a 1.5m long string and swung in a vertical circle with a constant speed of 12 m/s. What is the minimum speed the bucket can be swung at while still retaining the water. 2. The bucket has a maximum tension force on the string at the bottom, with 212 N...
  4. S

    Uniform circular motion - plane in a circular arc

    Homework Statement As a pilot comes out of a dive in a circular arc she experiences an upward acceleration of 9.0 gs (i.e. 9 x 9.8). a) Mentions that the Pilot's mass is 60 kg, already solved this b) If the speed of the plane is 330 km/h, what is the radius of the plane's arc...
  5. S

    Uniform circular motion proportionality question

    Homework Statement David spins a sling in a horizontal circle above his head. What would happen to the period of rotation if he applied the same force and the length was a) doubled, b) halved Homework Equations ac = (4π2r) / T2 The Attempt at a Solution Just not sure what to do in...
  6. S

    Uniform circular motion on a banked curve

    Homework Statement A car with mass 1200kg rounds a curve banked at 18 degrees. The radius of the curve is 130 m. Find the speed of the car if the frictional force between the tires and the road is 3.5 x 10^3 down the banked curve. Homework Equations ac = v2/r The Attempt at a Solution...
  7. T

    Static friction, uniform circular motion problem

    So I've been pondering on this question for quite a while and I'm a little stumped. It's not a homework problem; just a problem I came across yahoo answers a week ago. Basically it's a true or false question: Homework Statement If a highway curve is properly banked and posted at 45 mph, it...
  8. K

    What is the Speed and Maximum Height of a Pendulum Bob in Motion?

    A 1.0 N pendulum bob is set into motion on a 75 cm long string. At the bottom of the swing the tension is 1.2 N. a) Deduce that the speed of the bb at the bottom of the swing is 1.2 m s^-2 b) Determine the maximum height the bob will swing assuming no air resistance or friction...
  9. G

    Circular Motion - Pendulum Question .HELP

    Circular Motion - Pendulum Question...HELP! 1. A pendulum 80.0 cm long is pulled to the side, so that its bob is raised 20.0 cm from its lowest position, and is then released. As the 50.0 g bob moves through its lowest position, (a) what is its speed and (b) what is the tension in the pedulum...
  10. W

    Calculating Angular and Linear Speeds of a Rotating Disk

    Homework Statement A 3.5 inch floppy disk in a computer rotates with a period of 1.45 multiplied by 10-1 s. (Note: A 3.5 inch floppy disk is 3.5 inches in diameter.) (a) What is the angular speed of the disk? (b) What is the linear speed of a point on the rim of the disk? (c) Does a...
  11. R

    Radius of the path of an accelerating object in uniform Circular motion

    Homework Statement A 2 kg car travels in a flat circle. At a certain instant the velocity of the car is 24 m/s West and the total acceleration of the car is 9 m/s 2 at 53 degrees North of West. What is its radius? Answer in units of km. Homework Equations F=ma w=(2pi)/T a= w^2...
  12. G

    Circular Motion with Angular Speed dealing with planets

    1. Homework Statement Mars orbits the sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi) a) suppose Earth and Mars are positioned such that Earth...
  13. J

    CIRCULAR MOTION PROBLEM INVOLVING SPRING. In dire need of help please.

    1. Homework Statement A ball of mass m is connected by a spring shaft that is rotating with constant angular velocity (omega). A student looking down on the apparatus sees the ball moving counterclockwise in a circular path of radius r. When the spring is unstretched, the distance from the...
  14. J

    Circular Motion Problem With Static Friction

    1.Two metal cylinders of mass m1 and m2 are placed one at the top of the other on a circular turntable that is rotating at a constant speed as illustrated in the diagram. The coefficient of static friction between the lower cylinder and the turntable is s1 and the coefficient of static friction...
  15. I

    Uniform circular motion Lab

    In a lab we were supposed to produce a rollercoaster ramp while it had a loop, and then to drop a marble at a height where it would finish the entire path without falling off, with enough centripetal acceleration at the loop. we were not given the mass of the marble, and we were only given a...
  16. M

    Non Uniform Circular Motion Problem

    A new car is tested on a 200m diameter track. If the car speeds up at a steady 1.5 m/s^2, how long after starting is the magnitude of its centripetal acceleration equal to the tangental acceleration? So we know that our acceleration is equal to 1.5 m/s^2, our radius of our circle is 100m. I...
  17. N

    Circular Motion of ball tension

    Homework Statement In the device shown below, a 1.75 kg ball suspended by two cords is whirled around in a circle of radius 95 cm. The ball makes 10 revolutions in 2 seconds. Find the tension in each of the two cords (remember: the tension in each cord acts toward the pole)...
  18. W

    Uniform Circular Motion Space Station question

    Homework Statement A proposed space station consists of a circular tube that will rotate about its center (like a tubular bicycle tire), as shown in the figure (http://session.masteringphysics.com/problemAsset/1057181/4/GIANCOLI.ch05.p048.jpg). The circle formed by the tube has a radius of...
  19. W

    Circular motion - finding revolutions?

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  20. B

    Circular motion with unknowns and picture

    Homework Statement An ice cube slides on a frictionless sphere. It is placed at the top at of the sphere with radius (R), and given an instantaneous push at speed (S). At what angle(x) from vertical does the ice cube leave the surface of the sphere? Radius = R Speed/Velocity = v angle = x...
  21. M

    Circular Motion Concepts: Understanding the Stability of Rotating Objects

    Homework Statement how come that if I grab a stone and attach it to a string and then rotate it along the xy axis it won't fall even though there is acceleration from gravity in the z axis where no force is applied? Homework Equations The Attempt at a Solution maybe its the fact...
  22. C

    Magnitude of Friction Force - Circular Motion

    Homework Statement A car of mass 1164kg was traveling around a 288m radius corner at a speed of 10.8m/s. What was the magnitude of the fiction force required to maintain the vehicles path? Homework Equations F=ma I have no idea after that The Attempt at a Solution I found mg =...
  23. C

    Calculating Minimum Coefficient of Friction for Safe Rotor-Ride at Carnival

    In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "room". The room radius is 4.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? Attempt...
  24. L

    Nonuniform Circular Motion: The Top of the Loop

    If a ball is going through a loop-the-loop, at the top, if mg=m(v^2/r), it will continue around the loop. If mg>Fc, it will fall. In the first case, when mg=Fc, the normal force on the ball from the metal of the loop is 0. This is easy enough to see when the equation from the free body...
  25. D

    Finding the angle in a Uniform Circular Motion problem?

    1. Alright say you have a simple pendulum with given mass, length, and velocity (I think.. correct me if I'm wrong) ... how would I go about calculating theta (in degrees)? 2. I'm assuming the quadratic eq will have to be used? Among a couple of the simple force formulas. 3. I...
  26. K

    Circular motion and speed of rotation

    Homework Statement There's a 'chair-o-plane' with a radius of 4m and the seats are connected using 3m chains. a) Calculate the speed of rotation at which the chains make an angle of 35 to the vertical b) What is the tension in the chain if a rider of 90kg is on the swing at the speed above...
  27. S

    Circular Motion of space station

    Homework Statement 4) A circular space station rotates to provide an “artificial gravity” at the outside rim. a) If the diameter of the space station is 500m, how many revolutions per minute are needed in order for the “artificial gravity” acceleration to be 8.0 ms-2? b) If the space...
  28. D

    Related rates with circular motion

    Homework Statement I was really struggling with a Calculus problem but I think I have the right answer, this is more just checking with someone than anything. When given a Ferris Wheel has a radius of 10 m, and that it takes 2 minutes for one rotation, find how fast it is moving from the...
  29. P

    Circular Motion on a Ferris Wheel

    Homework Statement At a county fair, a boy and two friends bring their teddy bears on the giant Ferris wheel. The wheel has a diameter of 10.5 m, the bottom of the wheel is 1.7 m above the ground and its rim is moving at a speed of 1.0 m/s. The boys are seated in positions 45° from each...
  30. P

    Will I Slide in My Seat During a 2km Level Turn at 400km/hr in an Airplane?

    Homework Statement you are sitting in an airplane. you have a window seat. the plane makes a level turn of 2km at speed 400km/hr. the coefficient of static friction btwn you and the seat is .35 Then they ask is the frictional force sufficient to keep you moving in a radius of 1km at a speed...
  31. C

    Conceptual understanding of circular motion

    [PLAIN]http://img207.imageshack.us/img207/37/capturebg.jpg a=v^2/r v=2pir/T f=ma So I already have the answers to all the questions. The problem I am having is I don't understand why the centripetal force is not equal to the weight of the person. If it isn't the weight what...
  32. J

    Angle and Frequency in Horizontal Circular Motion

    Homework Statement What happens to the angle below the horizontal as frequency increases? (in horizontal circular motion) Homework Equations The Attempt at a Solution I think that it would decrease, because your speed is increasing, but I don't know if I'm right
  33. S

    Uniform circular motion - stone in pail

    Homework Statement A stone rests in a pail that is moved in a vertical circle of radius 60 cm. What is the least speed the stone must have as it rounds the top of the circle if it is to remain in contact with the pail? Answer: 2.4 m/s Homework Equations v= 2 pi r / t The Attempt at...
  34. J

    Maximizing Circular Motion Experiment Accuracy with Horizontal Tension Force

    Homework Statement For an experiment involving spinning an eraser horizontally on the end of a string. For the greatest accuracy in this experiment, the tension force on the eraser should be horizontal. In this context, assuming all other variables are constant, what happens to the accuracy...
  35. S

    Uniform circular motion mass problem

    Homework Statement A mass of 1.5 kg moves in a circle of radius 25 cm at 2 rev/s. Calcualte (a) the tangential velocity, (b) the acceleration, (c) the required centripetal force for the motion. Answers: A) 3.14 m/s B) 39.4 m/s^2 radially inward C) 59 N Homework Equations v=2piR/T...
  36. E

    Circular Motion and String Tension

    Working with circular motion ... Homework Statement Jill of the Jungle swings on a vine 6.9m long. What is the tension in the vine if Jill (63-kg) is moving at 2.4 m/s when the vine is vertical? Homework Equations T=mgsinθ Fc=m(v^2/r) The Attempt at a Solution T = (63)(9.81)...
  37. S

    Circular motion: bicycle moving in a circle. Find speed given r and degree

    Homework Statement A bicycle is racing around on a horizontal surface in a circle of radius 19 m. The force exerted by the road on the bicycle makes an angle of 23 degrees with the vertical. What is its speed? Homework Equations I believe this is a uniform circular motion problem, so...
  38. A

    Circular Motion with Vector Notation

    Homework Statement A particle is in uniform circular motion about the origin of an xy coordinate system, moving clockwise with a period of 7.00 s. At one instant, its position vector (from the origin) is r = (6.00 m) i - (3.00 m) j. At that instant, what is its velocity in unit-vector...
  39. R

    Finding the Optimal Initial Speed for Circular Motion - What's the Solution?

    this is the question. A ball is placed against the inner edge of a cylinder at a height h=4R where R is the radius of the cylinder. What initial horizontal speed v0 tangential to the cylinder wall should be given to the ball so that it will have completed exactly 2 revolutions around the inside...
  40. H

    Static Friction and Uniform Circular Motion

    Homework Statement A cat sits on a merry go round at a radius of 4.0m from the center. The ride makes one complete rotation every 6.3 seconds. What is the least coefficient of static friction to keep the cat in place? Homework Equations Circumference = 2Pi*r V=d/t a=v^2/r The...
  41. N

    Non-uniform circular motion question

    Homework Statement An object of mass m=.500kg is suspended from the ceiling of an accelerating truck. Taking a=3.00m/s^2 find the angle θ that the string makes with the vertical and the tension T in the string. Homework Equations The Attempt at a Solution mgsinθ=ma =>...
  42. M

    Uniform circular motion of a particle

    Homework Statement A particle's position is given by the formula r(t) = Rcos(ωt)î + Rsin(ωt)ĵ The particle's motion at t=0 can be described as a circle starting at time t=0 on the positive x axis. a) When does the particle first cross the negative x axis? b) Find the speed of the particle at...
  43. P

    Circular motion of a small block

    Homework Statement A small block sits 0.15 m from the center of a horizontal turntable whose frequency of rotation can be smoothly increased. If the coefficient of static friction between the block and the turntable is 0.55, at what frequency will the block begin to slide off? (Draw a force...
  44. C

    Lab for finding acceleartion vectors for circular motion

    Homework Statement I am trying to draw a change in velocity vector connecting from V1 to -V0, but I can't seem to figure it out. How do I show you guys what my problem is? Homework Equations N / A The Attempt at a Solution Googled for help
  45. J

    How Do You Calculate Path Length and Displacement on a Circular Track?

    Homework Statement An ant positioned on the very edge of a Beatles record that is 18.00 cm in radius revolves through an angle of 110.0o as the disk turns. What is the ant's path length? What is the magnitude of the ant's displacement? Homework Equations Ac=v^2/r T=2pir/v...
  46. tiny-tim

    Circular motion: static or dynamic friction?

    A simple question, but I can't find the answer anywhere :redface: … when something (otherwise unconstrained) is pulled by rope (approximately forwards) so as to slide (not roll) at constant speed in a circle on a rough surface, the total acceleration is obviously centripetal (radial) there...
  47. T

    Circular Motion - friction and tension problems

    Homework Statement A curve with a 125 radius on a level road is banked at the correct angle for a speed of 20. If an automobile rounds this curve at 30 , what is the minimum coefficient of static friction between tires and road needed to prevent skidding? Homework Equations F=ma...
  48. T

    Calculating the Speed of a Plane for a Stationary Sun at 26.3° Latitude

    Homework Statement How fast must a plane fly at a latitude of 26.3° so that the sun stands still relative to the passengers? Homework Equations I have no idea how I can solve this question. I would like to draw a free-body diagram, but I don't know how to do that either. If I could...
  49. P

    Circular Motion of a ball around the earth

    Homework Statement Calculate thow long it would take a ball to orbit the Earth once , just above the surface , at a speed of 7920 ms^-1 . The radius of Earth is 6400km. Homework Equations Well I am not sure to be honest. The Attempt at a Solution I tried using S=ut+1/2(a)(t)^2...
  50. D

    Non-Uniform Circular Motion - Finding total acceleration

    Homework Statement Homework Equations a(total) = sqrt( a(tangential)^2 + a(radial)^2 ) The Attempt at a Solution I wrote out equations for the forces in the radial and tangential directions: F(radial) = T - ( mg * cos(θ) ) F(tangential) = mg * sin(θ) I used the equations to find...
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