# What is Angular displacement: Definition and 68 Discussions

Angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis. When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the body's motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible. Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion.

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1. ### B Multiple Rotating Signs on a Fence Gate -- Overlap Question

Hey Everyone, This is a little project of mine. I'm including a daigram of it - top view -> down. This is part of a larger system. Consider a fence gate made of poles. In my diagram Point "A" in blue is a non-moving vertical pole. Point "B" red is a pivot point for an arm containing all...
2. ### Why Does Calculating Torque at the Ladder's Contact Point Not Work?

I am trying to get the torque about the point of contact of the ladder on the ground = mg x l/2, but it is not leaving me anywhere
3. ### What is the smallest value of angular displacement of the raft?

What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...
4. ### B Calculation of displacement of an object

Hi, this is my first time here. I'm and E&E student currently working on a project. I'm trying to calculate the overall displacement of my device given the X and Y displacement of the object and also the yaw heading of the device. The direction of the heading is the direction where the X axis...
5. ### Shape of graph of torque vs angular displacement of galvanometer

I know the torque will be zero when the deflection is zero and will be maximum when the angular displacement is θ0 but how to determine the exact shape of the graph? Thanks
6. ### Difference between gyroscope angular displacement and Euler angles

Hi guys, I'm trying to understand between gyroscope angular displacement and euler angles? for example { Δx = Δx + h * Rx * SCx);} this is gyroscope output about anguler displacement.This value can be used to determine angle that device created.Why we should euler angles to fly.(I know...
7. ### I 2nd derivative of angular displacement wrt time

If ##\theta## is angular displacement, does ##\frac{d^2\theta}{dt^2} = (\frac{d\theta}{dt})^2##? Proof?
8. ### Swing and angular displacement

hi, we are a few non-native English speaker physics teacher and we wrote some questions for an assessment book but we can't be sure about this two similar question. a) are they accurate for rules of English, are we use correct terms is there a necessary change? b) are they accurate for rules of...
9. ### I Controversy about the nature of finite angular displacement

Hello all, I am having hard time to know if the finite angular displacement really a scalar quantity? In some books they say angular displacement when finite is Scalar and when infinitesimal small is Vector, with direction perpendicular to plane of circle government by right hand rule. I...
10. ### Webpage title: Understanding Angular Displacement in Circular Motion

Homework Statement I play swing a yo yo above my head in a circular horizontal motion. The yoyo travels around 370 degrees. what is the angular displacement? Homework EquationsThe Attempt at a Solution would I say the angular displacement is 10 degrees? or still 370 degrees? or would both...
11. ### Angular Displacement: 2π Radians

I walk around a circular track. My displacement is 0 because I'm back at my starting point. How about my angular displacement? Is it 2 pi radians, or is it also 0? The definitions I've been reading online seem to indicate that 2 pi radians is the answer.
12. ### Why a finite angular displacement is not a vector?

One of my friend has answered this question in this way. Angular displacement can't be a vector because addition is not commutative. Say we are looking at the Earth with North America facing us and the North Pole facing up:if we rotate the Earth so that we move 90 degrees north, now the NP is...
13. ### Minimum Speed for Balsa Cube Tipping Problem

A solid balsa cube of side length L = 16.0” and mass M = 8.60 kg is at rest on a horizontal table top. It is constrained to rotate about a fixed and frictionless axis, AB, along one edge of the cube. A bullet of mass m = 50.0 g is fired with speed v at the other side of the cube, at height a =...
14. ### Converting Chord Length to Radians: A Confusing Concept?

Homework Statement Coverting Cord length to radians and the other problem is: A ball Radius = 12 CM, rolls 15 M, across the gym floor. Through what angle does the ball rotate? We just started this today and I am very confused by it. the other question is converting 11.6 CM Chord Length into...
15. ### How Do You Calculate the Shortest Flight Path Between Two Points on the Globe?

Homework Statement To attend the 2000 Summer Olympics, a fan flew from Mosselbaai, South Africa (34S, 22E) to Sydney, Australia (34S, 151E). (a) What is the smallest angular distance the fan has to travel: (1) 34 degrees (2) 12 degrees (3) 117 degrees (4) 129 degrees? Why? (b) Determine the...
16. ### Rotational motion: Find angular displacement when rotation speed is changing

Homework Statement A torque acts on a wheel rotating at 19.8 rad/s and increases its angular speed to 23.5 rad/s in 11.2 s. Find the angle through which the wheel turns during this time. Homework Equations omega = theta/time The Attempt at a Solution 23.5 - 19.8/11.2 = .33rad/s/s --- this is...
17. ### Understanding Angular Displacement in Weakly Damped Harmonic Oscillators

Hey PF. This isn't a homework question and I'm hoping this is the right place to ask it, sorry if it isn't! In the case of a weakly damped harmonic oscillator driven by a sinusoidal force of the form Fe^(iwt). The form of the differential force equation of motion is then given by ma + cv +kx =...
18. ### Relation between angular displacement and tension.

Hello guys, Iam doing a project to find the tension of timing belt using a dial gauge indicator(consists of plunger and gear attached to it ie;rack and pinion mechanism) ,but i can't find a formula relating the displacement of the pointer and the tension (eg: 5° of dislplacement of pointer =...
19. ### Formula relating angular displacement and tension.

Hello guys, Iam doing a project to find the tension of timing belt using a dial gauge indicator,but i can't find a formula relating the displacement of the pointer and the tension (eg: 5 deg of dislplacement of pointer = 10 units of tension).Please help me...
20. ### Rocker Output-Two Positions with Angular Displacement

This is a example from Robert L. Norton's books on machinery: "Design a fourbar Grashof crank-rocker to give 45° of rocker rotation with equal time forward and back, from a constant speed motor input. Solution 1)Draw the output link O4B in both extreme positions, B1 and B2 in any convenient...
21. ### Molniya Orbit: calc angular displacement of ascending node

Hello there :), Homework Statement We have a molniya orbit with an eccentricity of e = 0.72 and a semi-major axis a = 26554 [km]. The task: Calculate the angular displacement of the ascending node Ω after 100 sidereal days Homework Equations Moreover I know from Wikipedia that a...
22. ### Calculating Angular Displacement of CD with Radius 6.0 cm

Homework Statement If the radius of theCD below is 6.0cm and the angular velocity is 5.0 rad/s , what's is its angular displacement in 2.0s ? Homework Equations Delta θ = ωt+.5∂t^2 The Attempt at a Solution I know the angular velocity and the time but how can I find out the radial...
23. ### What is the proof that periods cancel out in finding angular displacement?

Homework Statement http://answers.yahoo.com/question/index?qid=20120411050123AA0ar9P Homework Equations [b]3. The Attempt at a Solution [/b Only I have one question concerning the answer that "E" provides in the link: why do periods cancel out?
24. ### What is the angular displacement of a thrown ball

Homework Statement A ball is thrown to a man and reaches him in 60s. The ball curves because it is spinning at an average angular velocity of 330 rev/min on its way to the man's hands. What is the angular displacement of the ball Homework Equations θ=ωt The Attempt at a Solution I...
25. ### Torsional oscillator with angular displacement

1. A torsional oscillator of rotational inertia 2.1 kg·m2 and torsional constant 3.4 N·m/rad has a total energy of 5.4 J. What is its maximum angular displacement? What is its maximum angular speed? Homework Equations θ(t)=Acosωt The Attempt at a Solution still trying to...
26. ### Question on circular motion, finding out the angular displacement in a clock.

Homework Statement A clock is showing 3.30. Calculate the angular displacement in degrees from the 12.00 position of the clock to: i the minute hand ii the hour hand I got my minute answer as 180 degree, which is right. But my second answer was 90 degrees, which apparently is wrong! the...
27. ### Angular Displacement Differentiation

Homework Statement An angular displacement θ radians in time t seconds is given by the equation θ = sin 3t. Find a:) angular velocity when t = 1 second b:) the smallest positive value of t for which the angular velocity is 2rad/s c:) the angular acceleration when t = 0.5 seconds d:) the...
28. ### Angular displacement of a curve ball

1. A pitcher throws a curveball that reaches the catcher in .60s. The ball is spinning at an average angular velocity of 330 rev/min, (assumed constant) on the path to the catcher's mitt. Find angular displacement. 2. θ=ωt where t is time, ω is angular velocity, and θ is angular displacement...
29. ### Graphical Analysis Question - Torque, Angular Displacement

Homework Statement The graph shows the behavior of an object with the moment of inertia of 18 kgm^2 a) Calculate the magnitude of the constant torque that acted on the system. b) Through what angle did the object rotate between t=2 and t=20 seconds? Homework Equations...
30. ### Double Slit Experiment - White Lite & Minimum Angular Displacement

Homework Statement A two-component beam of light, consisting only of two wavelengths 650 nm and 520 nm, is used to obtain interference fringes in a double-slit experiment. The separation between the centers of the slits is 2.43×10−4 m and the distance of the plane of the slits from the...
31. ### Emailanmol's discussion on angular displacement

Mod node: This thread was split from this other thread, 590162. Hey vkash. This is a good one. See, instantaneous angular displacement is a vector. Average angular displacement is not a vector.What does this information tell you about instantaneous angular velocity and acceleration...
32. ### Angular displacement is not a vector

Homework Statement The angular displacement θ, despite having a magnitude and a direction, cannot be treated as a vector. This is because θ does not follow the commutative law of vector addition. Does the infinitesimal displacement dθ obey the commutative law of addition and hence qualify...
33. ### Calculating Angular Displacement

Homework Statement I'm trying to calculate the angular displacement. A pendulum with length L is released at θ=0.10rad at 0s. Really not sure how to calculate the angular displacement from this. In a previous question we calculated the values of omega, and phi. Homework Equations I...
34. ### Angular displacement in radians

Homework Statement The radius of a wheel is 0.450 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 4.64 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. What is the angular...
35. ### Torque, Angular Displacement, Work

Torque, Angular Displacement, Work! Homework Statement The radius of a wheel is 0.525m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.45 N, unwinding the rope and making the wheel spin counterclockwise about its central axis. Ignore the mass...
36. ### Axial Vector: Small Angular Displacement

why is angular displacement considered an axial vector only for small values?
37. ### Finding Angular Displacement in a Pirouette

Hey, I have a very easy problem. A dancer completes 2.2 revolutions in a pirouette. What is her angular displacement? here's my work. Given: 2.2 revolutions. Battle Plan: Find angular position in radians. Subtract final position with the initial position. Outcome: 2.2 x 2pi = 4.4 pi...
38. ### Solving a Steam Engine Flywheel Angular Displacement Problem

Homework Statement The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.33 rad/s2. It accelerates for 23.5 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 67.3 s after it begins...

A fan rotating at 2.1 radian/s slows down with a constant acceleration and comes to a stop in a time of 4.7 s. What is its angular displacement in this time? Is this what I'm supposed to use: Δθ = Δθ2 − Δθ1? if it is I'm not sure how to begin to solve this problem, if anyone could help me...
40. ### Heisenberg Uncertainty Relations - angular momentum and angular displacement

Homework Statement Starting from one of the more familiar Heisenberg Uncertainty Relations, derive the Uncertainty Relation involving angular momentum and angular displacement and explain its significance. Homework Equations The relevant uncertainty relationship is that between...
41. ### Calculating angular displacement of clockhands

Homework Statement What is the a.d of each of the following hands of a clock in 1h? the second and? the minute hand? the hour hand? Homework Equations That's what I'm looking for The Attempt at a Solution I'm having trouble getting it on paper, just a description of how one of...
42. ### Infinitesimal angular displacement ?

How can we proved that the infinitesimal angular displacement is a vector mathematically ? Or~how can we prove that a non-infinitesimal angular displacement is not a vector ?
43. ### Max angular displacement from max angular velocity

Homework Statement A thin rod of length 1.4m and mass .2kg is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 7.84 rad/s. Neglecting friction and air resistance, find how far above that...
44. ### Angular displacement, velocity and acceleration

I have a few problems that I am very confused on. If someone could walk me through them that would be a big help. 1. An antique spring-driven Victrola phonograph plays recordings at 78 rpm. At the end of each record the arm hits a lever that activates a brake that brings the record to rest...
45. ### Pendulum - find maximum angular displacement

Homework Statement A 15-centimeter pendulum moves according to the equation: theta=0.2cos8t where theta is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of theta when t=3 seconds...
46. ### Pendulum - find maximum angular displacement

Homework Statement A 15-centimeter pendulum moves according to the equation: theta=0.2cos8t where theta is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of theta when t=3 seconds...
47. ### Angular displacement and bicyclist

1. An exhausted bicyclist pedals somewhat erratically, so that the angular velocity of his tires follows the equation omega(t) = 0.5t - 0.25sin(2t), t greater than/equal to zero. where t represents time (measured in seconds). 2. omega is defined as the first derivative of...
48. ### Angular Displacement: Earth's Orbit 2 Days

Homework Statement Earth's orbit around the sun is nearly circular. The period is 1 yr = 365.25 days. In an elapsed time of 2.0 days, what is Earth's angular displacement? Homework Equations Theta=Theta final - Theta inital The Attempt at a Solution I'm very confused and need...
49. ### Angular displacement & velocity

Homework Statement After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 7.05 rad/s and it rotated 13.7 revolutions before coming to rest. What was its average angular acceleration? Homework Equations ω2 = 2 alpha . theta The Attempt at a...
50. ### Rotational Kinematics Problem - find the angular displacement

Homework Statement The drive propeller of a ship starts from rest and accelerates at 2.90e-3 rad/s^2 for 2.1e3 seconds. For the nest 1.4e3 seconds, the propeller rotates at a constant angular speed. Then it decelerates at 2.3e-3 rad/s^2 until it slow (without reversing direction) to an...