# What is Angular motion: Definition and 82 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. ### Angular momentum of rotating hoop

Problem: Official solution: My calculation: \begin{align*} \mathbf L &= M \mathbf R \times \mathbf V + \mathbf L_{cm} \\ &= M R (\hat j + \hat k) \times (- \Omega R \hat i) + MR^2 \Omega \hat j \\ &= MR^2 \Omega (\hat k - \hat j + \hat j) \\ &= MR^2 \Omega \hat k \end{align*}
2. ### I Looking for a unified expression for energy in rotating systems

Hello, I am wondering if anyone can give me a hand. I am looking for a unified expression for energy in rotating systems or wondering if one even exists. Any help or equations you wish to share about the topic would be great. Sorry I am quite new to physics. Thanks
3. ### I Game Design: Set rigid body into a position (Euler angles) using angular velocity

I apologize for messy title, but that's as short as I could make it to say all that I wanted. I also apologize if I'm not using correct math phrases, but I'll try to picture a problem the best I can. I've been pulling my hair out trying to solve a problem I'm having for couple of months. The...
4. ### I Can angular motion exist outside of a gravity field?

I can't find the answer anywhere here's my question. can a centrifuge exist outside a field of gravity. More specifically, in a theoretical void of nothing without stars in view or any point of reference for comparison how could motion like spinning or acceleration exist?
5. ### Question about gravitational potential energy and angular motion

hello I would like some help with the first part of this homework. for the moment i have done this: E initial=m*g*h Efinal= 1/2 m*v ^ 2+1/2I*ω ^ 2 Ei=m*g*h+1/2I*ω ^ 2 Ef=1/2*m*v ^ 2 my doubt is with the potential energy since it confuses me when there is or not...
6. ### I The time for a tilted brick to hit the ground

I am interested in climate change and thereby interested in tipping points. So for the last few months, I have been investigating the dynamics of a toppling brick. I derived a differential equation of for the motion and wrote a computer program to solve this from initial conditions. I have more...
7. ### Energy Conservation in Angular motion / Moment of Inertia

I write Conservation of Energy: Potential Energy loss(change): U = m g ##\Delta##h = m g (R+r) (1-cos##\alpha##) kinetic Energy gain(change): K = (##\frac {m v^2} 2## + ##\frac {I \omega^2} 2##) + (##\frac {M v_2^2} 2## + ##\frac {I_2 \omega_2^2} 2##) U = K m g (R+r) (1-cos##\alpha##) =...
8. ### 1D Angular Motion with different velocity stages

Homework Statement I am solving a kinematic problem, where I have a link that is attached to a rotational joint. I need to find the position of the joint for t=0..8, and I need to do it for every 0.01s. The problem comes from the fact that I have three stages for the velocity, during t = 0..0.1...
9. ### Rolling with slipping and conditions for not slipping

Suppose that we have a some rotating object (lets say a wheel with radius R). Let's observe this problem from some reference frame in which center of mass translates with some velocity v and rotates with angular velocity ω. I know that condition for rolling without slipping is v=ωR (point at...
10. ### I Spinning bicycle wheel in air and letting it go

Let's say that we have a bicycle wheel with radius $R = 25 cm$ and mass $m = 1 kg$. We spin the wheel in air so, that the tread is moving at the speed of $v_o = 50 km / h$. Then, we let it roll on asphalt, given the coefficient of static friction: $f_s = 0.9$ and kinetic friction: $f_k = 0.7$...
11. ### Super quick question about angular motion

Homework Statement Homework Equations displacement = .5(wi+wf)*t wi =0 wf=5 rev / sec t=10 The Attempt at a Solution displacement = 5/2*10= 25 revolutions I know it is simple, but I am not sure if i heard right that the answer is actually 50 revolutions. Did i do something wrong?
12. ### Momentum transfer from linear to angular motion

I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...
13. S

### Circular Motion question, why does Fnet = 0 (so that T=W)?

Homework Statement A 0.50kg puck rests on a level air table and is connected by a light thread passing through a hole in the table to support a hanging mass of 3.0 kg. A stable orbit is achieved when the puck is sent into a circular path of radius 0.15 metres around the hole. (A) neglecting...
14. S

### Question about Angular Motion in a horizontal plane

For finding the critical speed or the minimum speed in a question for a vertical plane, you take either the friction or the contact (normal) force to be 0, so F=W However, for a horizontal plane, like spinning something around in a circle, you can still do F=W to find the critical speed or the...
15. ### Conservation of Angular Momentum with SHM

Homework Statement A 39.00 kg rod of length 2.8 m is hanging vertically by one of its ends that is free to swing in a complete circle about a frictionless axle/pivot. The rod has uniform mass density. Suddenly it is struck horizontally by a 5 kg putty that sticks to the center of...
16. ### A Supposition of Angular Motion

Suppose that angular momentum of mass M is equivalent to the angular momentum of the background universe spinning in the opposite direction from center of mass M. Suppose that the background's true rotation is un-observable. What would be the implications of such a supposition?
17. ### Can I use this solution? Angular motion

Homework Statement Starting from rest, a wheel has constant α = 3.0 rad/s2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval? ω0 = 0 α = 3.0 rad/s2 θf = 120 rad Homework Equations Δθ = ω0⋅t + ½αt2 The Attempt at a Solution 120...
18. ### Moment of inertia of a wheel: linear to angular motion

Homework Statement You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...
19. ### I About precessing directon of angular motion in quantum mechanics

Hi all, I got a feeling that learning quantum mechanics is easy and hard. Most of time, it is easy to "accept" all the concepts given in the book by simply looking at their mathematical interpretation. But it is hard if you really take it serious to try to understand everything from the...
20. ### Deriving to find speed (angular motion)

Homework Statement Going through a lecture recording from a lecture I missed the lecturer says "to get the relationship between translational speeds and angular velocities we will take a differential" what is that relationship she is talking about? does she mean converting between the two? The...
21. ### Conversion between two Harmonic Angular Motion

Homework Statement I need to find a way to do a conversion between the angular motion of a motor to the angular motion of an oscilating bar that is connected to it through a sliding and rotating collar. This way, every time the motor completes a revolution, the bar swings back and forth with a...
22. ### Acceleration around a running track

Homework Statement He is running around a running track training for a 400m race. His velocity is 5.11m/s around the circular end of the track, which has a radius of 31.8m. I'm trying to find his acceleration which I know is 0.821ms-2 but I can't find out how to get it. Homework Equations v=rω...
23. ### Collision involving angular and linear motion

Homework Statement a small 0.199 kg block slides down a frictionless surface through height h = 0.608 m and then sticks to a uniform vertical rod of mass M = 0.398 kg and length d = 2.23 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ. point O is at the end...
24. ### Angular Momentum and Conservation of Angular Motion

Homework Statement How much torque is needed to change the speed of spinning rate of a 3.50 kg sphere with a radius of 7.50 m from 900. rpm to 200. rpm in 3.0 s? [-1924  -1.92 x 103 Nm] Homework Equations t = I * α I = (2/5)mr^2 t = F * r The Attempt at a Solution just can't get a crack at...
25. ### Conceptual question on angular momentum and Emech.

Homework Statement A 60.0 kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 500 and radius 0f 2.00 m. Turntable is initially at rest and is free to rotate around frictionless vertical axle through its center. Woman then starts walking around the rim at...
26. ### Angular motion problem question

Homework Statement A homogeneous cylinder of mass 1.20 kg and diameter 25 cm rolls down an inclined plane that makes an angle of 25 degrees with the horizontal. What is the speed of the axis of the cylinder by the time the cylinder has rolled 1.00 m down the plane? Homework EquationsThe...
27. ### Converting units for angular motion

I think angular velocity can be measured in radians/second. I also heard that if I multiply a value of angular velocity that is in the units of Rad./sec. by a certain value of radius in meters, I will get m/s, but this is the instantaneous tangential velocity. Is any of these right? In...
28. ### Angular motion-centrifuge problem .

Homework Statement : A centrifuge starts from rest and speeds up at 3400rpm after 50 seconds. a sample is at a distance of 37.5mm from the centre 1) find the angular acceleration 2) calculate the centripetal acceleration [/B] Homework Equations : v2 / r v = rω a = rω2 a=Λω/Λt 3. The...
29. ### What is the notation for angular distance travelled?

What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?
30. ### Relative angular velocity in a rotating rod

Consider a rod AB rotating about one of it's end A with angular velocity w. Now angular velocity of each point of the rod is same i.e. w. But if we have to find the relative angular velocity of the end B w.r.t. mid point of rod, what it will be? Will it be zero because, w-w=0 or first we...
31. ### Desperate for help -- studying an angular motion problem

hi folks, my back story is that I have failed my strength of materials and dynamics twice. the college I am attending put these courses in an accelerated time frame... this means 14 weeks of material turned into 7 weeks of material. I am not able to learn at that pace, hence why I failed twice...
32. ### Angular Velocity and Position: How to Solve Basic Angular Motion Problems

Homework Statement Homework Equations ω=ω0+αt θ=θ0+ω0t+12αt2 I think? The Attempt at a Solution For part a, I know that from the graph, the angular velocity in this case would be constant since the graph illustrates a position in rad vs time graph. The thing is, I'm really sure on how to...
33. ### Linear and Angular Motion Help

Homework Statement Need a bit off help with these questions would appreciate some help. Homework Equations 1. An accelerating vehicle crosses a datum with a velocity of 20m/s and then covers a distance of 2.5km in 50s. Calculate the acceleration, and the velocity reached after it has traveled...
34. ### How do you determine the angle turned by a winding drum with given data?

1. A mine cage of mass 1.5 tonnes is accelerated uniformly upwards from a speed of 1.1 m/s to 4.6 m/s in a time of 20 seconds. The winding drum which is 1.5 metres in diameter has a mass of 1.2 tonne and has the dynamic characteristics of a disc. There is a bearing friction torque of 48 Nm. For...
35. ### A question about angular motion

If a bead slides frictionlessly along a wire on a horizontal table. The wire is in the shape of a spiral, and the bead is given an initial push at the outer side of the spiral, so that it slides along in an "orbit" of decreasing radius.Is the bead going faster as it moves inward? Is its energy...
36. ### How Does Angular Motion Affect the Centrifugal Force on a Motorcar Wheel?

A mass of 5g is required to balance a motorcar wheel. If the mass is attached to the 0.33m diameter wheel rim, calculate the centrifugal force acting on the rim of the wheel. The speed of rotation is 521 rev/min.ω= 2∏N/60 F= M ω2 T ω=2∏*521/60 = 54.6 rad/s F= 5*10-3*(54.6)2*T I am not sure...
37. ### Angular Motion Conceptual Question

Hey all, in physics right now I am learning about rigid body rotations about a fixed axis. One of the questions we had for homework goes like this: "The combination of a friction force and applied force produces a constant total torque of 36 N*m on a wheel rotating about a fixed axis. The...
38. ### Is Velocity in Angular Motion Referring to Tangential or Angular Speed?

Hello, I was solving some problems today. Sometimes the wording is something like this: A ball attached to a string is traveling around a circular track with velocity 4 m/s. etc. When it says the velocity is 4 m/s , does this mean the tangential, or angular velocity? what is...
39. ### Analyzing Angular Motion of a Ferris Wheel

Homework Statement Starting from rest, a ferris wheel of diameter 30.0m undergoes an angular acceleration of 0.040 rad/s^2. A certain rider is at the lowest point of the wheel just as it starts to move. a)find the velocity of the rider just as he completes a quarter of a turn. b)find the...
40. ### How Do You Calculate Angular Motion for a Child on a Merry-Go-Round?

Homework Statement Okay so this is a multi part question. I think I am on the right track, but I am most likely wrong. Any help is good. If I know what to use for the equations I can usually solve it on my own. The question is: A child of mass 40kg is on a merry go round. The ride is a...
41. ### Problems of statics, angular motion and simple harmonic motion

All Questions are shown on pictures. My Calculated answers: A1(a) R= 19.21∠68.7o N (b) E = 19.21∠-111.34o N or = -19.21∠68.7o N <--- Is't either one answer is correct or not? If not, which answer is correct and why? Thanks. A2(b) I = 0.5mr2 = 1.125kgm2 A2(a) k=(I/m)1/2 = 0.212m...
42. ### Angular Motion Of A Bullet Striking A Door

The problem is: "A 0.00600-kg bullet traveling horizontally with a speed of 1.00*103 m/s enters an 19.2-kg door, imbedding itself 8.60 cm from the side opposite the hinges as in the figure below. The 1.00-m wide door is free to swing on its frictionless hinges. (a) Before it hits the...
43. ### Energy and angular motion problem

Homework Statement In the figure below, the hanging object has a mass of m1 = 0.355 kg; the sliding block has a mass of m2 = 0.840 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of...
44. ### Angular motion of a weather vane. How fast is it spinning after impact (rpm)?

Homework Statement A weather vane sits quietly on the roof of a barn on a calm winter's day. It has a length of x, is pole-shaped with mass M, and rotates frictionlessly about its center. But just now it is still. Suddenly Justin throws a snowball of mass m at speed v that hits it a...
45. ### Angular Motion: Solving for Velocity & Acceleration

Homework Statement A wheel 1m in diameter is rotating on a horizontal plane in the clockwise direction with an angular speed of 115 rpm. It's angular acceleration is 18 rad/s2 A) What is the angular velocity (magnitude and direction) after 6 seconds B) What is the tangential velocity of a...
46. ### Relationship between Rectilinear and Angular Motion

I am having a hard time understanding this concept... I understand Rectilinear motion consists of a line and Angular Motion is of a Angle. But I can't seem to understand how to use this for problem solving. I have two examples here that I will give and I have the answers but I can't seem...
47. ### Determining revolution using Angular Motion

Homework Statement The combination of an applied force and a friction force produces a constant total torque of 35.0 N · m on a wheel rotating about a fixed axis. The applied force acts for 5.90 s. During this time, the angular speed of the wheel increases from 0 to 10.1 rad/s. The applied...
48. ### Angular Motion and Young's Modulus

Homework Statement A mass of 13.0 , fastened to the end of an aluminum wire with an unstretched length of 0.50 is whirled in a vertical circle with a constant angular speed of 130 . The cross-sectional area of the wire is 1.3×10−2 . The Young's modulus for aluminum is Pa.Calculate the...
49. ### Calculating Tension and Angular Motion in a Pivoted Beam System

Angular motion + Inertia [SOLVED] Homework Statement A uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the...
50. ### Moment of Inertia & Angular Motion of a Stick

A stick of uniform density with mass M = 7.5 kg and length L = 1 m is pivoted about an axle which is perpendicular to its length and located 0.12 m from one end. Ignore any friction between the stick and the axle. a) What is the moment of inertia of the stick about this axle? Iaxle = kg...