Uniform circular motion Definition and 312 Threads

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. J-dizzal

    Uniform circular motion problem

    Homework Statement A police officer in hot pursuit drives her car through a circular turn of radius 356 m with a constant speed of 70.9 km/h. Her mass is 57.1 kg.What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider...
  2. J-dizzal

    Uniform circular motion of a particle problem

    Homework Statement A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s)## \hat j ## and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity...
  3. J-dizzal

    Particle Uniform circular motion problem

    Homework Statement A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s) ## \hat j ##and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity...
  4. T

    Tension and Uniform Circular Motion (no r, ω, θ)

    Homework Statement A 0.020-kg mass is attached to a 1.2-m string and moves in a horizontal circle with a constant speed of 1.50 m/s, as shown in the figure. What is the measure of angle θ? What is given: m = 0.020kg v = 1.50 m/s L = 1.2 m Homework Equations Lengths L = 1.2m Lsinθ = r...
  5. kostoglotov

    Uniform Circular Motion: a concept question

    Homework Statement A particle moving along a straight line can have nonzero acceleration even when its speed is zero (for instance, a ball in free fall at the top of its path). Can a particle moving in a circle have nonzero centripetal acceleration when its speed is zero? If so, give an...
  6. B

    What is the instantaneous velocity of an object moving uniformly in circles?

    Homework Statement An object is moving uniformly in circles with a radius of 5m and a frequency of 2 Hz. What is its instantaneous velocity? Homework Equations [/B]The Attempt at a Solution The problem i am dealing with is the frecuency. I am not here for an answer or to cheat. I am...
  7. T

    Conceptual Uniform Circular motion problem?

    Homework Statement This isn't a homework problem, but I was just thinking of the following question: Suppose that a merry go round spins with a constant speed (so its radially accelerating towards the center), and a man want to jump onto the merry go-round while its spinning. In what way...
  8. 1

    Uniform Circular Motion question

    1. The problem The answer is A. Homework Equations x = Acoswt y = Asinwt The Attempt at a Solution C is not correct because the x & y positions are in terms of sin & cos, so the acceleration can't be constant. D is not correct because x & y are oscillating in value. E is not correct because...
  9. S

    Uniform Circular Motion and Projectile All-in-One

    Homework Statement \[/B] Joey spins a laptop then he releases it, at an angle. Assuming no wind resistance, the laptop (has a rubberized case) hits the concrete and drags across the concrete for 5.3 seconds. What is the coefficient of friction between the rubber and concrete and what distance...
  10. A

    Calculating Tension in a Hypothetical Moon-Earth System

    Homework Statement Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth. Find the tension in the cable. Homework Equations F=ma a=v^2/r v=2πr/T (since the pictures aren't working, I'm just going to post the url to the image)...
  11. parabola

    Help with high school dynamics assignment?

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > I've searched for help before posting, found this thread that is asking for the same assignment by unfinished so I'll just copy and paste lol...
  12. A

    Uniform Circular Motion Background theory?

    Hi Guys, new poster here. I am currently doing a practical report on Uniform Circular Motion, where we had to swing a rubber stopper around attached to a length of string and mass. I have to do a write up, including the background theory. I have searched everywhere but I have found no clear...
  13. P

    Average velocity in uniform circular motion

    Suppose a particle undergoing uniform circular motion completes a cycle, then ##<\vec{v}> = \frac{Δ\vec{r}}{Δt} = \vec{0}##. But then again, isn't it also the mean of the two velocity vectors at that point? And aren't those two velocity vectors equal? So if the velocity at that point were, say...
  14. C

    Dot product in uniform circular motion question -- Finding angle?

    I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...
  15. D

    Work in Uniform Circular Motion

    Uniform circular motion requires a force perpendicular to the velocity. Therefore, the work done by such a force is zero because the dot product of the force and the path is zero. So there is no energy gain beyond the kinetic energy arising from its constant speed. But if I have a mass (rocket...
  16. A

    Why they don't give me the same answer? dynamics of uniform circular motion

    Homework Statement So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass Homework Equations P = mg , didnt know what to put here The Attempt at a Solution So this is what the book did. What I...
  17. cseil

    Uniform circular motion for proton and 2 particles

    [Note by mentor: This thread does not use the homework template because it was moved here from a non-homework forum.] Hello, I have a problem with this exercise. I don't know if my solution is right! Could you check it, please? A proton with kinetic energy Kp is moving in a uniform magnetic...
  18. Ludwig

    Uniform Circular Motion puzzle

    The position function for a particle moving on a circle (with constant speed) is: ## \vec{r}(t)=\left \langle r\,sin(t), \, r\,cos(t) \right \rangle ## Taking the first and second derivatives, ## \vec{v}(t)=\left \langle -r\,cos(t), \, r\,sin(t) \right \rangle ## ## \vec{a}(t)=\left \langle...
  19. P

    Uniform Circular Motion on a race track

    Homework Statement On a banked race track, the smallest circular path on which cars can move has a radius of 116 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.6 m. Find (a) the smallest and (b) the largest speed at which cars can move...
  20. P

    Uniform Circular Motion of a centrifuge

    Homework Statement 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...
  21. G

    Uniform Circular Motion of a Spherical Earth

    Homework Statement In this question, the Earth is modeled as a uniform sphere of radius 6400km. Objects are released from points just above the Earth's surface at the equator and at the North Pole. Which will fall to the Earth with the greater acceleration and by how much? Homework Equations...
  22. A

    Velocity of an Object in Uniform Circular Motion

    Homework Statement An object of mass 0.5 kg is swung in uniform circular motion. The radius is 2 meters, and the force exerted is 4 N. Calculate the magnitude of the velocity. Answer Choices: a) 0.25 m/s b) 1 m/s c) 4 m/s d) 16 m/s Homework Equations v = 2piR/T F = mv^2/R The Attempt at a...
  23. P

    Uniform Circular Motion: Why is the velocity changing?

    I encountered this question in a practice test for an upcoming exam. My first inkling was to answer with (C) because in uniform circular motion, the acceleration always points towards the center of the circle, but the actual answer was D. Do you think this question was just an issue of direction...
  24. Ascendant78

    Would a uniform circular motion frame be inertial if ω is constant?

    I'm wondering if someone is observing a situation from a frame moving in a uniform circular motion, would that frame of reference be considered inertial? I'm unsure because of the centripetal acceleration towards the center.
  25. I

    How to Add Acceleration Vector in Uniform Circular Motion

    Currently we're discussing uniform circular motion in my physics class. The previous unit discussed vectors and vector addition in the i, j, k format. When I try to apply the rules for vector addition to find the resultant velocity in uniform circular motion, I get an increase in the...
  26. S

    Uniform Circular Motion vs Circular Orbit due to Gravity

    In uniform circular motion, (eg, a mass on the end of a string moving in a horizontal circle) centripetal force is the only thing causing acceleration. we have the kinematic relationship V=RW or velocity is proportional to radius. I.e a bigger radius means greater linear speed? For the...
  27. matineesuxxx

    When Does Radial Acceleration Equal Tangential Acceleration in Circular Motion?

    Here is the problem I am working on: A steel ball is accelerated around a circular track of radius 72 cm from rest. after 3 circuits the ball reaches a speed of 4.00 m/s, assuming tangential acceleration, a_{T} , is constant, how long after the ball starts moving is radial acceleration, a_r ...
  28. G

    What is the normal acceleration of body in non uniform circular motion

    when the body rotates with uniform motion then the normal acceleration is V^2/r. but what is the normal acceleration when the motion is in non uniform circular motion let's say when body has uniform tangential acceleration.
  29. Nathanael

    Uniform Circular Motion and Centripetal Acceleration

    In introductory physics books (or at least mine) it limits the equation a_c=\frac{v^2}{r} to the sitaution where the speed around the circular path is constant. It enforces the idea that the speed is CONSTANT. But wouldn't the equation also apply to non-constant speeds? (a_c would just...
  30. Govind_Balaji

    Velocity of uniform circular motion

    Homework Statement The minute hand of a clock is 4cm long. Find the average velocity of the tip of the minute hand between 11.00 am to 11.30 am. (in m/s)Homework Equations The Attempt at a Solution 1.In the motion between 11 am to 11.30 am, \theta=180^o=\pi \text{radiaans}\\ radius=4cm\\...
  31. C

    Uniform Circular Motion amusement park ride

    Hello everyone, I'm really stuck on this question. The diagram shows an amusement park ride which contains a carriage attached to a mechanical arm. This arm spins around full circle. The carriage has a mass of 300 kg and a maximum occupancy of 300 kg. The question asks: With its carriage...
  32. A

    Uniform Circular Motion and Centripetal Force

    Hey guys, first post here! Hoping to get a little help. Homework Statement You are a traffic safety engineer in charge of determining safe speeds for roads. A particular banked curve has a radius of 11.0 meters and is banked at an angle of 8.00°. The coefficient of static friction between...
  33. P

    Uniform circular motion and angular momentum?

    Homework Statement A sphere on top of a table is attached to a rope which goes through a hole in the table and is attached to a bucket at the other end. The sphere moves in a uniform circular motion with radius R. Water is then added to the bucket and the radius for the sphere's circular...
  34. C

    Three charges q, uniform circular motion

    Homework Statement Two spheres have a charge of q a stationary sphere between them has a charge of -q. The 2 positive spheres move like conical pendulums at a constant velocity of 12.0m/s in uniform circular motion. What is the magnitude of charge q? Homework Equations Electric Force...
  35. S

    Time dilation and uniform circular motion

    Hi, I've taken a course in SR and studied GR on my own, but I do not know how to solve problems of this type. This is just purely for fun, not homework related at all. A particle of mass m is moving on a circle of radius R at constant linear velocity v = .8c. If the particle makes N...
  36. Ascendant78

    Gravity and uniform circular motion involving a loop?

    Homework Statement A 0.27 kg toy car is held at rest against a 1796 N/m spring compressed a distance of 8cm. When released, the car travels a distance of 112cm along a flat surface before reaching a 0.30m high loop. The friction coefficient of the flat surface and the toy car is (0.4...
  37. R

    Uniform circular motion and tension of a string

    Homework Statement a 0.60 kg sphere rotates around a vertical shaft supported by 2 strings, as shown. if the tension in upper string is 18N calculate. a) tension in lower string? b) rotation rate (in rev/min) of the system. Homework Equations The Attempt at a Solution...
  38. Q

    Uniform Circular Motion: Solving for String Tension

    Homework Statement A ball of mass 4 kg on a string of length 1.5 m is being swung in a circle in the vertical plane at a constant speed of 10 m/s. Find the tension in the string at the bottom and top of the balls path Homework Equations ƩF = m(v^2/r) The Attempt at a Solution This is how I...
  39. S

    Particle in uniform circular motion

    Homework Statement A satellite is orbiting 600km above the Earths surface. The free fall speed is 8.21 m/s^2. The radius of Earth is 6400km. What is the satellites speed, and the time interval for one orbit around Earth. Homework Equations v = ((2)(PI)(r))/T ac = rw^2 w = (2)(PI)...
  40. P

    Calculating Acceleration in Non-Uniform Circular Motion

    Homework Statement The Attempt at a Solution So I just want to ask any of you who know physics pretty well if I am on the right track on this question, so it is asking for the magnitude of the acceleration of the car, and the direction. The magnitude of acceleration is (v^2/R) v = velocity and...
  41. B

    Uniform Circular Motion A Jet Pilot

    Uniform Circular Motion "A Jet Pilot" Hi, my apologies if this has been posted before. I was just wondering if someone could help look over this question for me and confirm if I did it correct or not. It is a written homework rather than online so I can't check my answer to see if I did it...
  42. skate_nerd

    MHB Proofs regarding uniform circular motion in vectors

    Just started this Analytical Mechanics class, so I figured this question should go here... I've been pretty stuck with a problem. I felt like I totally knew what I was doing but I've become very stumped. We're given the vector for general circular motion...
  43. M

    Doubt in uniform circular motion

    why are we considering speed is constant to find velocity a particle in uniform circular motion, is it possible for a particle in a circular motion to have constant velocity?
  44. J

    Is uniform circular motion perpetual?

    If i took my pencil to a place in space without gravity or air resistance and i spun it, would it spin forever? I mean its undergoing a centripetal acceleration, so energy has to come from somewhere to keep it spinning right? (and of course this is not meant to be an idea for perpetual motion, i...
  45. andyrk

    Radial acceleration in uniform circular motion

    Why is there only a radial component of acceleration present if a body is undergoing uniform circular motion whereas in non uniform circular motion both tangential and radial component of acceleration are present?
  46. N

    Uniform Circular Motion extended response

    This began as homework that our Physics teacher set us. However, for some reason he decided no to collect it. I am curious as to whether or not this display my understanding of the topic well as communication is main area my teacher believes I need improvement in. Homework Statement Write a...
  47. andyrk

    Understanding Uniform Circular Motion: Exploring Centripetal Acceleration

    In uniform circular motion only a radial component of acceleration is present i.e centripetal acceleration. So why doesn't the particle following uniform circular motion go radially inwards due to radial acceleration?
  48. Nugso

    Uniform Circular Motion

    Homework Statement An object is in uniform circular motion. As the time passes by, its mass decreases. ( It has Co2 in it, and it evaporates) What will happen to the object's velocity and angular momentum? Homework Equations F = mV²/r, L = mvr The Attempt at a Solution...
  49. A

    Uniform Circular Motion Question (Mechanics/Physics I)

    Uniform Circular Motion Question Please Help! (Mechanics/Physics I) A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.10. The length of the arc ABC is 200 m, and the car completes the turn in 34.0 s. (figure attached as...
  50. A

    Direction of force acting on a body in uniform circular motion?

    Direction of force acting on a body in uniform circular motion?? Hello Sir/Ma'am I'm a a novice. I joined this forum to clear my doubts and improve my physics. Here is my question.. " We generally say, frictional force always acts in a direction, opposite to the direction of motion of a body...
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