# 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. ### Tension & Circular Motion Question - Looking for speed

I have attached a screenshot of my rough work. First of all, is my interpretation of the question correct? Please see the diagram in purple. To me, this makes sense because a=v^2/r is the only equation from my coursework that seems to relates radius (which you can find from the length of the...
2. ### I Origin of Centripetal force when the net force toward the center is 0?

to clarify , my purpose isn't to find a solution to my home work , I already did the home work and my thread is more a request of justification or at least a clarification of the forces at play. I need explanation on the general topic not the solution to my question, I am mentioning the question...

4. ### B Why is speed constant when centripetal acceleration is constant?

It's actually getting little boring and makes me angry why all the videos/articles show centripetal acceleration formula and presume that speed is constant. I want to prove backwards, i.e we know the constant perpendicular force acts on an object from the center and why object starts to move in...
5. ### 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:
6. ### The advisory speed for a car on a sloped bend

Hello all, I am sadly stuck on the last part of a circular motion question sheet I was given for homework. I have a mark-scheme with me, but it has actually given me more questions than answers. I have attached my working, and how I arrived at my answer, and the differences it has with the...
7. ### Circular Motion: A coin on a rotating disk

I believe I've solved this problem, however, I got through it pretty quickly and since it's the last problem on the assignment, I feel that I may have had an oversight. For part a, I got: fs=md(α^2)(t^2) and for part b, I got: ω=Sqrt((µs*g)/d) Could someone confirm my answers? I've attached a...
8. ### Circular Motion - Newton's Second Law: Bead on a Rotating Hoop

For whatever reason, I'm having a hard time conceptualizing this problem. I understand that the tangential components of all forces involved need to cancel out in order for the bead to be stationary. I also understand that there is a mgsinθ in the negative θ-hat direction. What I don't...
9. ### Angle of acceleration in non-uniform circular motion

For (c), Solution is Can someone please explain how they calculated that angle? I thought they would do ##arc\tan (\frac {32}{3.35})## Many thanks!
10. ### Is the Instantaneous Circle Proven When Centripetal Force is Removed?

Can someone show that the instantaneous circle is indeed given by when the centripetal force is removed? This can be found at https://www.vedantu.com/iit-jee/circular-motion
11. ### Circular Motion with Decreasing Radius

The answer key states that the new tangential speed is half the original speed. However, this isn't correct right? It should double. My proof: ##F_c = \frac {mv^2} R## ##F_c = F_t## ##\frac {mv^2} {\frac R 4} = \frac {m(2v)^2} R## If centripetal force were to stay constant. As such, tangential...
12. ### How to find Vmax squared for circular motion?

T= m*vmax^2/r 1500 = (80kg)vmax^2/4.5
13. ### Inelastic collision followed by circular motion

Found the speed at which the masses will travel after their collision: 2.25m/s Not sure what to do next...
14. ### Normal force at the top of a vertical loop -- Circular Motion Dynamics

From the equation for centripetal force, I can see that the centripetal force is proportional to v^2. Does this have something to do with why there is a normal force at the top? Does the velocity of the object require there to be a normal force? If so, why is that the case?
15. ### Acceleration of the cart on a Ferris Wheel (Circular Motion)

After 3,32 seconds, vt should have varied by 0,695*3,32. I have done a previous exercise where you only needed to calculate the radial acceleration in this scenario. There, I took the vt after the given time, squared it and then divided with the radius. I remember clearing that one, so in this...
16. ### Help with, I am sure, a really simple circular motion problem

Summary: I am just trying to go through a Brilliant physics unit. I came across this axe throwing question which I don't get at all how they get the answer. You can see the answer there. So their explanation is; 'In going around the circle, the red point moves through an angle of θ =...
17. ### Can you explain the correct way to choose axes for circular motion analysis?

Haii, I don't understand why I need to choose my n-t components in the direction of a circular motion and can't just use them with the n-axis along the rope and the binormal perpendicular to the surface.
18. ### Solving a Circular Motion Problem - Expert Tips and Techniques

Could someone please help me solve this?
19. ### I Velocity for uniform circular motion

Hello everyone, I've been studying centripetal and centrifugal acceleration and derivation of their magnitude. I noticed in one of Walter Lewin's lectures that the velocity is written as both a vector and an arc length which is confusing to me. When velocity is written as a vector, it has a...
20. ### Deviation of Plumb Bob In Uniform Circular Motion

I started by making my coordinate system so that the x-axis aligned with the radius of the circle at a certain latitude L and the positive direction was facing away from the center of the circle, and the y-axis was parallel to the vertical axis of the Earth. Then, I wrote the equations for the...
21. ### Relativistic particle in uniform magnetic field (solution check)

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...
22. ### Heavy mass vs light mass in circular motion

i think that the light sphere will go up higher(will have bigger acceleration) because there has to be a balance between the mass and the acceleration as long as the force is the same, for example if you push a heavy object and with the same force pushed another light object the light object...
23. ### Circular motion to projectile motion

So first I found the velocity of the ball at the bottom of the swing from the force equations, which I got to be 4.9 m/s and this is only in the x-direction. Then using the projectile motion for delta y I found time, which is 0.2s. Then using that time I found the delta x to be 0.98m. I just...
24. ### Find the acceleration in circular motion

Hello , First of all , I am still new to circular motion or any motions in general and still relatively learning so please bear with me. 1 . The direction of the tangential acceleration is parallel to the net velocity and that of radial of perpendicular to the velocity. So the direction of net...
25. ### B Gravitational acceleration in circular motion

Hi guys, I have a question that is simple but I do not know how to answer that. It is the following, where does the acceleration of 9,8 meters per second squared go when We're dealing with uniform circular motion? I know that We have the centripetal acceleration that is a vector change, but the...
26. ### Circular Motion Problem -- Ball on a String Spinning in a Vertical Circle

#F= m\frac{v^2}{r} = mw^{2}r# #m=5# #r=0.9# #F= 5\frac{v^2}{0.9} = (0.9)5w^{2}# #5\frac{v^2}{0.9} = (0.9)5w^{2}# #\frac{v^2}{0.9} = (0.9)w^{2}# #v=0.9w# then I get stuck cause I have both unknowns in one equations (i bet it has something to do with the question’s use of “minimum” but I...
27. ### Tetherball rope wrapping around a pole

My work so far is pretty basic, but I'm not too sure how to continue off from here. I haven't included the 2 dimensional aspect of it either, but I would presume that the rate of decrease in length is more sped up in that case? Would appreciate any help :(
28. ### Car that undergoes non-uniform circular motion

In the solution manual, it says that: the resultant of friction force is ##<= kmg##, hence $$m\sqrt{\omega_t^2 + (\frac {v^2} {R})^2} <= kmg$$ and from this equation, we will get $$v^2 <= R \sqrt{(kg)^2 -\omega_t^2}$$ which will make ##v_{max}^2= R \sqrt{(kg)^2 -\omega_t^2}## Finally, they...
29. ### Another Doubt From Halliday Resnick Krane -- Puck on a string in circular motion

Hello! This is a problem from Halliday Resnick Krane (Chapter 4: Problem #15). “A puck is moving in a circle of radius r0 with a constant speed v0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is...
30. ### B Resultant force in vertical circular motion

Suppose we have a vertical circular motion with gravity according to the image below. In the leftmost and rightmost positions the resultant force is pointing diagonally down. Isn't the resultant force supposed to be pointing at the center at all times in a circular motion? What am I getting...
31. ### What is the meaning of work done for non-uniform circular motion?

This is my solution ,and I just use the definition .But I still feel unclear about the concept of non-conservative force.$$W = F x = 30N (\frac{1}{2}\pi r ) = 56.2 J$$ $$E_{system} = \Delta K + \Delta U = W$$ $$(K_{f}- K(i))+(U(f)-U(i)) = W$$  (\frac{1}{2} *m{V_{f}}^2...
32. ### How to calculate differential work done by a force in circular motion?

My question is, is this correct, and if so, why the minus sign?

34. ### Circular motion of a mass on a string on an inclined plane

(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing) I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...
35. ### Tension of string acting on stone moving in horizontal circular motion

Is it possible for the stone to move in horizontal circular motion just like in the picture? I try to draw the free body diagram of the stone and there are two forces acting on the stone, its weight (directed downwards) and the tension of the string (directed to the left). The tension will...
36. ### B Confusion while trying to build intuition of centripetal force

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then...
37. ### I Non-uniform Circular Motion & Acceleration

I would really appreciate some help with this problem regarding non-uniform circular motion, in which a body is accelerating as it follows a circular path. If we take Example 1, a body starts at Point A with an angular speed of 180°/s. The body accelerates to Point B and reaches it some time...
38. ### Would particle P be under non-unform circular motion?

At t= 0, we can see that the particle P has a radial acceleration of ##-2\hat j## and a tangential acceleration of ##2 \hat i##. The radial acceleration will tend to move it in a circle of a certain radius, whereas the tangential acceleration will tend to displace it parallel to x- axis...
39. ### How to get gravitational force on a gaseous particle?

This question is very confusing since I don't see two distinct particles that are exerting a gravitational force on each other. Also to complicate matters, a gas is made of many individual particles and I don't know how to determine the gravitational force on a single particle from so many other...
40. ### I Determining Future Position of Uniform Circular Motion

Hello, Apologies if this is in the wrong section, it's related to circles so I figured Geometry was the best place. I found a very good example online that explains how to determine a future position of an object undergoing uniform circular motion: (Note that they made a mistake by writing...
41. ### Tension in rope for non-uniform circular motion with air resistance

I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that mar = (m(v)2)/r. I'm failing to understand how mg and the drag force affects the solution and how I would set it up. I know if it was at the bottom of the circle that mg would be added to the...
42. ### A Car on a Banked Curve Moving in Uniform Circular Motion

First I figured out the normal force being exerted on the car using the equation above. Cos(40°)*(1050*9.8) = 7883N Next, I tried to find out the horizontal component of the normal force by doing: Cos(50) * 7883 = 5067N I figured out the angle by using certain geometrical properties. Next, I...
43. ### Constant Circular Motion Not Really Constant

I was pondering my practice of talking about circular motion in the horizontal direction and the vertical direction. But I'd often would see in books, notes, and the internet that we assume constant velocity for the vertical case. However, when one thinks about the forces at different points in...
44. ### Circular Motion Questions (energies, forces, angular velocities, etc.)

Question 1: I believe that the ratio would be b. 8:1 because by combining the formula for kinetic energy and momentum the expression Ek=p^2/2m can be obtained. Thus, for a body of mass 2kg with twice the momentum: Ek=2^2/2*2=1 For a body of mass 4kg with half the momentum: Ek=1^2/2*4=1/8...
45. ### What is the angle between the acceleration and velocity when rotating?

##ω = \frac {k} {\sqrt{φ}}## What is the angle between acceleration and velocity after 1spin (2π radians)? First I decided to find out what is the angular acceleration: ##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = -...
46. ### Circular motion of a particle around a track -- what provides the centripital acceleration?

Suppose a particle is moving around a circular track of radius R at speed v. To bend around a circle some agency has to exert an acceleration towards the center of the circle. I analyze the forces acting on the particle, its weight and the normal force and there is no acceleration in the...

Help please
48. ### Uniform Circular Motion on a racetrack

Not sure what I'm doing here. Not sure how to continue? Please help. Thank you in advance!
49. ### Uniform Circular Motion: banked race track circular path

Basically, I need help to continue on this question. This is what I have now: Angle of the race track (angle of the grey part): tan(18/(169-108)) = 0.30396 Not sure how to continue?? What am I supposed to do and find next? Thank you in advance! :smile::blushing::oldbiggrin:
50. ### What is the reaction force between the ring and the hoop?

a.)N cos θ=mg N sin θ=mrw^2 sin θ cos θ=g/rw^2 b.) My question is reaction force =N ? or =F=mg tanθ ? If it is N then N=mg cosθ =mg^2/r w^2 or N=mg/cosθ =mrw^2 ? Thank you