# What is Angular speed: Definition and 278 Discussions

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function.
Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.One revolution is equal to 2π radians, hence

ω
=

2
π

T

=

2
π
f

,

{\displaystyle \omega ={\frac {2\pi }{T}}={2\pi f},}
where:

ω is the angular frequency or angular speed (measured in radians per second),
T is the period (measured in seconds),
f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν).

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1. ### Question involving angular acceleration of a spinning wheel

wfinal=98.0 rad/s, dt=3.00s w=(37 revs/3)=>w=(37 revs*(2*pi/1))/3=>w=77.493 a=(98-77.493)/3=>a=6.8357 My answer is exactly half of the correct answer. Where did I go wrong?
2. ### Angular speed of rod shot by bullet

1) Applying conservation of linear momentum: $$m.u = M.V + m.v$$ where ##V## is final linear speed of the rod $$V=\frac{m.u-m.v}{M}$$2) Applying formula of circular motion: $$V=\omega . r$$ $$\omega = \frac{\left(\frac{mu-mv}{M} \right)}{\frac{1}{2}L-x}$$ Is this correct?And can this be...
3. ### Finding angular speed geometrically

So clearly the easiest way to relate the angular speed to the linear speed would be to start from ##\tan(θ) = x/h## and take a time derivative of both sides. However, it also shouldn't be difficult to find the angular speed geometrically. Using the diagram below one can see that: ##sin(dθ) =...
4. ### Angular speed of a falling rod

I have seen the solution and understand it. The solution defines θ to be the angle between the falling rod and the table. It then equates initial PE to the final (PE+KE) where the final PE=0 and the final KE to be (1/2) Iω2+ (1/2) ma2ω2 to finally obtain ω = √(3g/2a) But i would like to know...
5. ### Spring-mass system in circular motion has a maximum angular speed?

and this is my solution for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$ but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large Besides, I don't know other Physics prevents...
6. ### Hinged Rod- angular speed

The centre of mass of the rod would be at the middle of the rod i.e. at l/2=[50*10^(-2)]/2 The force responsible for torque will be acting downwards = mg The Torque = mg*l/2*sin(30) =mg*l/4 We know that Torque=I*alpha Hence alpha = mg*l/(4*I) Moment of inertia of rod about the end= ml^2/12 +...
7. ### Kinematics and angular speed of a collision between a rod and puck

initial total KE= (1/2)(0.6kg)(8m/s)^2 = 19.2J (0.6kg)(8m/s) = (0.6kg+1.8kg)(vf) vf= 2m/s final KE= (1/2)(0.6kg+1.8kg)(2m/s)^2 = 4.8J I tried to use linear speed=angular speed * radius : thus 2m/s= angular speed * (3.3m/2) angular speed= 1.2 rad/s Apparently that is wrong.
8. ### Angular speed, acceleration, and angle of a Ferris wheel

ω(10)=(1.3)∗(1.0−e^(−10/22) )= 0.475 rad/s 0.475 rad/s=0 +α(10second) α=0.0475 rad/s^2 ∫ω(t)=Θ =1.3t + 28.6e^(-t/22) | (t=10s, t=0) total angle by which the wheel rotates over this period of t=10 seconds = 2.55 rad Θ= 2(pi)(8m)= 1.3t + 28.6e^(-t/22) 0=1.3t + 28.6e^(-t/22) - 2(pi)(8m) t=34...
9. ### Angular and orbital speed at perihelion

Hello to all good people of physics forums. I just wanted to ask, whether the angular and linear (orbital) speed in perihelion of eliptical orbit are related the same way as in circular orbit (v = rw). If we take a look at the angular momentum (in polar coordinates) of reduced body moving in...
10. ### Finding Angular Speed and the Change in Kinetic Energy

(4+.9)(Wf)=(4+.63)(.27) (4.9)(Wf)=1.2501 Incorrect
11. ### How to calculate angular speed?

Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...
12. ### MHB Frequency and Angular Speed

Hello there, I'm new here and i need some help on my home work. A DVD drive rotates at an angular frequency of 4800 rpm. a) what is it's angular speed in rpm? b) at 4800 rpm, what is the linear speed (in knm/hr) of (i) the center point and points (ii) 5 cm and (iii) 6 cm from the center? Thanks!
13. ### Angular speed that breaks a spinning body apart with inertial stress

How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)? I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) ...
14. ### Find the angular speed?

Homework Statement A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30 degrees with the horizontal...
15. ### What is the angular speed of the rollers after 1.14 s?

Homework Statement A plank of wood sits on top of two rollers with radius of 44.4 cm. The plank is pulled forward so it moves at a constant acceleration of 2.24 m/s^2, starting from rest, and the rollers roll without slipping along the ground and in contact with the plank. What is the...
16. ### Angular speed calculation after an inelastic collision

Homework Statement A disk [m=0.1 Kg; R=0.1 m] rotates about its center of mass [w=40 rad/s], on a smooth floor. A bar [m=0.1 Kg; lenght=R=0.1 m] moves on the floor with a speed Vb=4 m/s. At one point, the bar hits disk's edge in an inelastic collision, and they start rotating together. A)[Fixed...
17. ### Freezing of water inside a hollow sphere which is rolling

Homework Statement If we have a hollow ball completely filled with water which is rolling without slipping on a horizontal ground. If the water freezes which of the parameter will remain unchanged- angular speed, angular momentum, linear momentum, kinetic energy, total energy Homework...
18. ### MHB Angular speed of 2 pulleys on a belt

The two pulleys connected by a belt have a radii of 15 cm and 8 cm. The larger pulley rotates 24 times in 36 seconds. a. Find the angular velocity of the small pulley in radians per second. b. Find the linear velocity of a point on the belt that connects the two pulleys in centimeters per second.
19. ### Riding a bicycle around a tree w/ constant acceleration

Homework Statement African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a tree this size. If, starting from rest, you travel a distance of 162 m around the tree with a constant angular acceleration of 5.00 × 10–2 rad/s2, what will your final angular...
20. ### How to find Angular Speed when given frequency?

Homework Statement A floral clock in Japan has a radius of 15.5 m. If you ride a bike around the clock, making 16.0 revolutions in 4.50 min, what is your average angular speed? Homework Equations ω = velocity/radius ; 1 rev=2*pi rad The Attempt at a Solution (16 rev*2*pi rad)/270 secs = 0.372...
21. ### MHB A torsional pendulum - determine angular speed

A torsional pendulum made by suspending a horizontal uniform metal disk by a wire from its center. If the disk is rotated and then released, it willexecute simple (angular) harmonic motion. Suppose at t seconds the angular displacement of \theta radians from the initial position is given by the...
22. ### MHB Angular Speed of Smaller Wheel

Let r = radius See picture. If r = 6 cm, R = 10 cm, and the angular speed of the larger wheel is 100 rpm, determine the angular speed of the smaller wheel in radians per minute. Again, 1 revolution = 2 pi radians. I need to use w = θ/t. So, θ = 100 rpm • 2 pi radians. θ = 200 pi...
23. ### MHB Angular Speed of Smaller Wheel

I decided to change the radius. Let r = radius If r = 10 cm, R = 50 cm, and the angular speed of the larger wheel is 100 rpm, determine the angular speed of the smaller wheel in radians per minute. What are the steps to solve this question?
24. ### Find the angular speed of the smaller gear

1.Why does the angular speed of small gear depend only on larger gear only? 2.Why does the length of linkage connecting two gears does not have any influence on the angular speed of smaller gear? The first question can be answered by looking at slack and tightening of chain caused by rotation...
25. ### Computing angular speed wrt CM I get a contradiction

Hello! I have been brushing up my Rigid Body Dynamics. I tried computing the angular speed with respect the Center of Mass (CM) using the usual split of kinetic energy and also the split of Angular momentum using the CM. First, a simple case: Two particles of mass M each separated by a distance...
26. N

### Centripetal Acceleration Problem: Finding Angular Speed

Hi all, I've been lurking around the forums for a while to get help with homework but I figured I'd finally make an account to get direct feedback. I'm having problems with this centripetal acceleration problem, Homework Statement "In an old-fashioned amusement park ride, passengers stand...
27. ### Determine the angular speed ##\dotθ## of the arm OC

Homework Statement 13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0, determine the angular speed ##\dot θ## of the arm OC in terms of v0, b, and θ. Homework...
28. ### Finding angular speed by conservation of angular momentum

Homework Statement Homework Equations Angular momentum = moment of inertia * angular velocity Change in angular momentum = impulsive moment v^2=u^2+2as The Attempt at a Solution First I used v^2=u^2+2as to find the velocity of the particle the moment the string goes taut. I got v=\sqrt{8ag}...
29. B

### Rotation problem - AP Physics 1

Hey guys, I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page: So a couple of questions here: (By the way, I know the answer is C) 1. My teacher explained that the net torque here on the assembly would be zero(will ask him again later). Is this...
30. R

### Finding the Time of Max and 0 Angular Speed

Homework Statement Mod note: Fixed thread title. OOPS NOT Acceleration, Speed! (Thread title is incorrect) Homework Equations w=d∅/dt v=rw x={+,-√(b2-4ac)}/2aThe Attempt at a Solution I solved this with help from Chegg study, however, I'm still not entirely sure what I am doing. Obviously, for...
31. S

### Solid sphere rolling down a house roof.... angular speed

Homework Statement A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees. What is the angular speed about its center as it leaves the house roof? The height of the outside wall of the house is...
32. ### Time required for disk to reach angular speed?

Homework Statement A uniform disk of mass M = 3 kg and radius r = .22 meters is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1 n * m What is the time required for the disk to reach an angular speed of 800 rpm...
33. ### Points on a rigid body always have the same angular speed?

Consider a circle rotating about a point X on its circumference at ##\omega = 2## rad/s. That means all points on and in the circle rotate at the same ##\omega = 2## rad/s. What are the angular velocities of various different points, say points A, B and C, with respect to the centre O of the...
34. ### Can you get the inertia from the angular speed?

Homework Statement Homework Equations ... The Attempt at a Solution I've been searching for the relation between the spinning speed and inertia in equation form. I do know that since the skater inertia is smaller the spinning speed is faster but that about it. Any hint would be helpful. One...
35. ### Confusion about angular speed and angular acceleration

In my textbook.In some question gives me angular speed as ( )rev/s.I know that its the frequency (f).But some questions It says angular velocity and says rad/s. Interesting thing happens when the textbook says in angular speed and I use f and then using w=2πf and then continue I get wrong...
36. ### Rod+mass rotating clockwise

Homework Statement The 3.0 kg rod has a length of 80 cm. The 4.0 kg rectangle attached to the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal...
37. ### Rubber Band Spinning in midair

Homework Statement A uniform thin circular rubber band of mass M and spring constant k has an original radius R. Now it is tossed into the air. Assume it remains circular when stabilized in air and rotates at angular speed ω about its center uniformly. Derive an expression for the new radius...
38. ### Orbital vs. Angular speed

Is there a difference between orbital speed and angular speed when an object or star is considered to be in a circular motion around another?
39. ### Find the angular speed at t=3 seconds

Homework Statement A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds? t=3 seconds wi= 65.0 rad/s α =...
40. ### Dynamics problem: Crankshaft angular speed?

Homework Statement Homework Equations Kinematic theorems: The Attempt at a Solution Ok, I'm trying to use another angle, phi, and find some relation betwen phi and theta so I can derive the equation for the angular velocity of rod B with respect to S, but I'm stuck at that point. How...
41. ### Angular speed of the pulley

Homework Statement Homework Equations v=rω conservation of energy The Attempt at a Solution I don't know whether it is correct or not, and I am quite confused in part b it asks the angular speed of the pulley can I say that v=rω since the pulley and box A,B have a common velocity? so is ω...
42. ### Relative angular velocity

Homework Statement A particle of mass ##m## rotates about ##Z-##axis in a circle of radius ##a## with a uniform angular speed ##\omega##. It is viewed from a frame rotating about the ##Z-##axis with a uniform angular speed ##\omega_0##. Find the centrifugal force on the particle. Homework...
43. ### Kinematics angular speed

Homework Statement I have chosen my axis as you can see on the picture. To the left, it is the positive 'r'-axis, up is the positive 'y'-axis. I have to calculate the angular speed. My solution is correct, but I'm getting into trouble at the end. I have to take the roots of the last equation to...
44. ### Finding angular speed of disk

Homework Statement You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest...
45. ### Instantaneous angular speed question

Homework Statement How do you calculate instantaneous angular speed?[/B]Homework Equations I have been told that it is when delta t approaches 0, so its just the derivative of delta theta over delta t.[/B]The Attempt at a Solution does it involve tangent line like normal instantaneous...
46. ### Angular Speed and Kinetic energy

Homework Statement Ok I have the answers to parts a and b, which I am 100% confident in since they are simple computations Question is in attachement a)74.9 rad/s b)168.08 rad My issue comes in when I have to get parts c The mass of the cylinder is 8.7kg, its diameter is .18m, its .35m long...
47. ### Ratio of angular speed with conservation of energy

Homework Statement A ball rolls down an incline plane without slipping. What is the ratio of its angular velocity at h/3 to its angular velocity at 2h/3? 1) 1:2 2) 1:sqrt(2) 3) 1:1 4) sqrt(2):1 5) 2:1 Homework Equations Conservation of energy with provisions for rotational and...
48. ### Angular speed ratio and gear teeth ratio

http://www.tech.plym.ac.uk/sme/mech226/gearsys/gearaccel.htm Hello, I tried to derive n=N1/N2=omega2/omega1 with using T1=T2 but it is a wrong assumption. I thought they should balance to satisfy Newton's 3rd law, but it is not. Could you explain me why.
49. ### Determine the angular speed theta_dot

Homework Statement Homework Equations Vθ = r x θdot Vr = rdot Accelθ = r ⋅ θdot^2 + 2(r dot)(theta dot) Accelr = r double dot - (r ⋅(θdot)^2) The Attempt at a Solution I know that the answer is supposed to be But I'm not quite sure on how I'm supposed to get to an answer like that. I'm...
50. ### Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

Homework Statement A wheel spins at an angular speed of 2.50 rad/s for a total of 30.0s. How many complete revolutions will the wheel make during this time? A) 31.4 rev B) 19.3 rev C) 11.9 rev D) 75.0 rev Homework Equations W=Wo+(alpha)(t) θ=θo+Wot+1/2(alpha)t^2 W^2=Wo^2+2(alpha)(θ-θo) The...