# What is Uniform circular motion: Definition and 311 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. ### I Why can centripetal force balance out gravity?

I can't upload image, so the problem is the same as the summary: When an object is doing uniform circular motion in a plane parallel to the ground, the centripetal force is parallel to the ground while the gravity is vertical to the ground, so the combination of the two force must be downwards...
2. ### 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...
3. ### 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...
4. ### I Direction of friction of each wheel and total moment when a car turns

Static friction is known to provide centripetal force when a car turns. Assuming uniform circular motion, my questions are 1. Is the static friction of each wheel points toward the center of turning circle or it's the combined forces of all four wheels that has to point toward the center of...
5. ### I The centripetal acceleration of the planets in our solar system

Relevant formulae:- Angular velocity in uniform circular motion ##=## ##\omega## ##=## ##\frac {2\pi} t##, where ##t## is the time taken to complete one revolution. Centripetal acceleration in uniform circular motion ##=## ##a## ##=## ##\omega^2r##, where ##r## is the radius of the circular...
6. ### An electron enters a magnetic field

Hi, I tried to solve this exercise but I'm not sure about the process. First of all, I imposed that "K = E": so that "v = √ ( (2q ∆V)/m))" then I replaced in "r = m v / (| q |B)", v with "√ ( (2q ∆V)/m))", and found out that R = (2√(2)) r. Then for the second point, I imposed Lorenz Force...
7. ### 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...
8. ### 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...
9. ### Uniform Circular Motion on a racetrack

Not sure what I'm doing here. Not sure how to continue? Please help. Thank you in advance!
10. ### 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:
11. ### What happens when a car turns?

A car moving at constant speed is in uniform circular motion, thus having centripetal acceleration of ##a=\frac{v^2}{R}##. The force associated with this acceleration is known to be friction. But friction, in nature, appears as an opposition to the relative motion between two surfaces whether it...
12. ### Radial acceleration derivation with minimal knowledge

Just started learning about uniform circular motion. I really don't understand how we get aΔt2/2 on the side. I also searched on the internet for a similar derivation, but there are none so simple. Thanks for your help! P.S There is a mistake in calculation in second line (textbook error).
13. ### Circular Motion: Write expression for the period in terms of r and g

I'm not sure if I'm doing this right as far as coming up with the equation they are asking for. I feel the question is poorly worded and the formatting makes their equation notation difficult to understand. Any insight would be very helpful. This is my work so far:
14. ### Uniform Circular Motion: some help with the math proof?

I can not understand why ##v_x = -|v|sin(θ)## and ##v_y = |v|cos(θ)## I'm asking about the θ angle. If i move the vector v with my mind to the origin i get that the angle between x'x and the vector in anti clock wise, it's 90+θ not just θ. So why is he using just θ? Does the minus in v_x somehow...
15. ### Uniform Circular Motion, Find the Tension

IMPORTANT! TEXT IN GREEN HAS BEEN ADDED AND IS CORRECT TEXT IN RED HAS BEEN REMOVED AND IS INCORRECT 1. Homework Statement Question: An energetic father stands at the summit of a conical hill as he spins his 25 kg child around on a 5.7 kg cart with a 2.3-m-long rope. The sides of the hill are...
16. ### The Importance of Understanding Different Formulas in Uniform Circular Motion

https://i.imgur.com/4nynNBg.png I cannot understand for the life of me why this problem doesn't just use T = 2πr/v to solve for the period to get T = 2π(Lsinβ)/v. Instead, it rearranges the formula for a(rad) = (4π^2R)/T^2 to solve for T, and arrives at a totally different answer, T =...
17. ### Uniform Circular Motion question

Homework Statement While learning to drive, you are in a 1 320-kg car moving at 34.0 m/s across a large, vacant, level parking lot. Suddenly you realize you are heading straight toward a brick sidewall of a large supermarket and are in danger of running into it. The pavement can exert a...
18. ### Uniform Circular Motion and Projectile Motion Help

Homework Statement A 60 g ball is tied to the end of a 40-cm-long string and swung in a vertical circle. The center of the circle is 150 cm above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at the...
19. ### Uniform circular motion and conservation of energy

A point mass in an uniform circular motion is continuously changing the velocity direction. To do it, it continuously need force (energy). If we don't give any energy to the system it will anyhow continues its uniform circular motion. How it's possible, who gives the energy ? (It's seems a...
20. ### Uniform Circular Motion and Centripetal Acceleration (non-intuitive)

I'm in the chapter of Uniform Circular Motion and I have a hard time understating centipetal acceleration. Until now I knew that acceleration describes "how fast velocity changes in magnitude" except projectile motion because when it reaches maximum height then g is going to change the direction...
21. ### Uniform circular motion question

1. Homework Statement In picture Homework Equations f=ma v^2/r The Attempt at a Solution ΣFy=-mg - Fn = m(-v^2/r) -55*9.8 - Fn = m(-v^2/r) v= 16π/4.5 since circumference = 2πr divide by the rotations time taken per second = 11.17m/s -Fn = 55(-15.6) + 55*9.8 Fn = -319 What am i doing wrong here??
22. ### How does radius affect frequency in uniform circular motion?

I am writing a lab report on the effect of the radius of a string on the frequency of rotation on an object in horizontal uniform circular motion. My hypothesis is: If the radius of the string from the origin of rotation increases, then the frequency will decrease because frequency has an...
23. ### Difference between radial and centripetal acceleration?

Homework Statement I'm not understanding the difference between them, this is for Uniform Circular Motion. Homework Equations ar = -ac = -v2/r The Attempt at a Solution So what i know is radial acceleration goes in a direction towards the radius (perpendicular to velocity), and tangential...
24. ### Uniform circular motion - origin of speed

I am having trouble understanding tangential speed as it applies to uniform circular motion and I would appreciate any help. Say I have a ball on the end of a string that I hold with my hand and rotate at a constant speed. If the string provides the centripetal force and acceleration, where...
25. ### Uniform Circular Motion of Roller Coaster

Homework Statement Assume the roller coaster cart rolls along the curved track from point A to point C under the influence of gravity. Assume the friction between the cart and track is negligible. What would be the direction of the carts acceleration at point A? (The question in the image does...
26. A

### Uniform Circular Motion - distance

Homework Statement An object with mass m = 2 kg is moving in a uniform circular motion with radius r = 2m as shown in the figure. It takes π seconds for the object to travel from θ =0 to θ = 180 degrees. What is the distance traveled by the object in 20 s...
27. A

### Finding speed on a banked turn

Homework Statement The question wants us to find the velocity that the car can take without assistance from friction. The friction, in this case, is the normal friction, weight friction, and the static friction (pointing towards the right). I understand how it got ncos(15) - w = 0 for the y...
28. ### Non uniform circular motion acceleration

In uniform curved motion , I can get the acceleration from the equation : A = v2/r , but in non uniform the velocity is changing , so will the certipetal acceleration also change ?
29. M

### Uniform Circular Motion Inside a Sphere of Charge

Homework Statement "*Question 44: Uniform Circular Motion Inside Sphere of Charge The tau particle is a negatively charged particle similar to the electron, but of much larger mass - its mass is 3.18 x 10-27 kg, about 3480 times the mass of the electron and about twice the mass of a proton or...
30. ### Uniform circular motion -- How can radial acceleration have a calculated value?

In uniform circular motion, direction of particle is changing at every moment but its speed remains the same. If the magnitude of velocity or speed remains the same, change in magnitude of velocity is zero. Then how come radial acceleration can have a calculated value since acceleration = change...
31. ### Uniform Circular Motion, Acceleration problem

Homework Statement A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat’s velocity is V1 = (3.00 m/s)i + (4.00 m/s)j , measured on a horizontal xy coordinate system. At t2 = 5.00 s, the cat’s velocity is V2 = (3.00 m/s)i + (4.00 m/s)j. What are (a) the...
32. ### Magnitudes and Directions In Uniform Circular Motion

Homework Statement A biker is 40.0m to the east of a flag in a park, heading south at 10m/s. 30.0 seconds later, the biker is 40.0m north of the flag and heading east at 10.0m/s. For the biker in this 30.0s interval, what are: a) the magnitude and direction of the displacement? b) the magnitude...
33. ### Understanding Uniform Circular Motion: A Guide to Solving Problems

:H:H:H1. Homework Statement Homework Equations equations is not needed here The Attempt at a Solution I have no idea :( Please help me![/B]
34. ### Uniform Circular Motion Problem. Help

Homework Statement A stone tied to a string with length 1.10 m is whirled in a circle both horizontally and vertically with the same constant speed. In the vertical case the maximum tension in the string is 15.0% larger than the tension that exists when the string was horizontal. Determine the...
35. ### Uniform Circular Motion Problem

Homework Statement 1. A car is safely negotiating an unbanked circular turn at 21 m/s and the maximum static force acts on the tires. Suddenly a wet patch on the road reduces the static frictional force by a factor of three. At what speed must the driver slow to in order to safely continue on...
36. ### Calculating velocity needed for uniform circular motion?

Homework Statement "Figure 8-32 shows a pendulum of length ##L=\frac{5}{4}m##. Its bob (which effectively has all the mass) has speed ##v_0## when the cord makes an angle ##\theta_0=40°## with the vertical. (a) What is the speed of the bob when it is in its lowest position if...
37. ### Is Δθ in a circle equal to the angle in a velocity vectors triangle?

How is Δθ in circle equals to angle in velocity vectors triangle? I tried using simple geometry but I can't.
38. ### Centripetal Acceleration formula derivation

Hello, This is a very basic question. I am sure I am doing something wrong in the derivation as shown in the picture. But I am not able to find out where I am doing it wrong. It would be very helpful if you can pls. let me know what I am doing wrong here. Thanks
39. ### Uniform circular motion - finding velocity

Homework Statement Homework Equations radial acceleration = v^2/R The Attempt at a Solution I'm unsure if we have to mention the tension of the cable, but I'm guessing L2 will suffice? Correct me if I am wrong. Anyways, I drew the diagram from a side view (kind of like a circular pendulum)...
40. ### Projectile and Uniform Circular Motion

Homework Statement An object is launched horizontally from the highest peak on the Moon's surface. Calculate (a) the launch speed required so that the object travels completely around the Moon and returns to its original position, and (b) the time required to return to the launch point. Assume...
41. ### Roller coaster - uniform circular motion

Hi, I have been studying up on circular motion in the vertical plane and I am happy with all the math/theory that I have read explaining the normal force and weight force and the feeling of being "heavier" and "lighter". My question is about the top of the hill/ride, The forces acting on you at...
42. ### Finding radial & tangential acceleration at a point

Homework Statement A point on a rotating turntable 20.0cm from the center accelerates from rest to final speed of 0.700m/s in 1.75s. At t=1.25s, find the magnitude and direction of (a) the radial acceleration, (b) the tangential acceleration, (c) the total acceleration of the point. Homework...
43. ### Uniform Circular Motion and Centripetal acceleration

Homework Statement For a scene in a movie, a stunt driver drives a 1.20✕ 103 kg pickup truck with a length of 4.65 m around a circular curve with a radius of curvature of 0.333 km (Fig. 7.29). The truck is to curve off the road, jump across a gully 10.0 m wide, and land on the other side 2.96 m...
44. ### Uniform Circular Motion for rubber stopper

Homework Statement Picture- https://flic.kr/p/zi1ays The rubber stopper will be spun at a constant speed in a horizontal circle. The hanging mass is only in contact with the string.[/B] A) For the rubber stopper, state the forces and what they are exerted by and on B) Does the net force have...
45. ### Understanding centripetal force

I don't have a specific homework assignment, but rather my problem is with the general concept. I don't understand the forces acting in uniform circular motion. As I understand it, the force is directed inward, and there is no other force in the same dimension (in an idealized model). But in my...
46. ### Motion On An Off Center Circle In Polar Coordinates

Homework Statement A particle moves with constant speed ν around a circle of radius b, with the circle offset from the origin of coordinates by a distance b so that it is tangential to the y axis. Find the particle's velocity vector in polar coordinates. Homework Equations (dots for time...
47. ### Is Centripetal Acceleration Constant in Uniform Circular Motion?

Homework Statement i was going through uniform circular but a confusion popped out of my head . as i have read before the Rutherford atomic model was only rejected due to the fact that electrons moving in circular orbits need to accelerate constantly to maintain a uniform speed but the...
48. ### Uniform Circular Motion of coffee cup

Homework Statement Kim has her coffee cup on her car's dash when she takes a corner with radius 4 m and 20 km/h. What is the minimum coefficient of static friction which would allow the coffee cup to stay there without slipping? Homework Equations Can someone show me the steps in how they...
49. ### Uniform circular motion with friction

I recently took an exam in my engineering mechanics class and passed the exam except for one question. I have been trying to solve this question after the fact and determine the solution, however neither I nor several engineering tutors have had any success. The professor refuses to give...
50. ### 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...