Angular speed Definition and 278 Threads

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. H

    Find the angular speed of a cylinder with a spring

    Homework Statement A cylinder of radious r=10cm and mass m=1Kg is attached to a spring of constant k=18N/m. In every moment the cylinder rolls without slipping over the inclined plane with an angle of 30º. The other extreme of the spring is attached to a fixed point O, as shown. If the...
  2. N

    What is the Angular Speed of an Automobile Engine?

    Homework Statement . The angular speed of an automobile engine is increased at a constant rate from 140 rad/s to 200 rad/s in 20 s. The number of radians through which the engine turns during this 20-s interval is Homework Equations The Attempt at a Solution I didnt know...
  3. E

    What is the Angular Speed of Tires with a Radius of 31 cm and a Speed of 12 m/s?

    Homework Statement The tires of a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 12 m/s? Homework Equations w=θ/t The Attempt at a Solution θ=d/r θ=d/31
  4. M

    Angular speed and angular velocity

    hi i have two different systems (i have tried to upload them but they both exceed the size of the upload limit). One is a dc motor block diagram (it has a PID at its controller) the other is a bldc motor model with a PID controller input. The block diagram of the DC motor consists of an armature...
  5. Z

    How Do You Calculate the Angular Speed of a Billiard Ball After a Strike?

    A billiard ball is cued by striking it horizontally at a distance d=10mm above the center of the ball. The ball has mass m=0.2kg and radius r=30mm. Immediately after the strike, the center-of-mass of the ball moves with linear speed v=1m/s. Find the angular speed of the ball immediately after...
  6. R

    Kinetic energy of body rotating at constant angular speed

    Homework Statement A straight wire has uniform density and total mass M. The wire is bent to form a closed loop, one section of which is a semi-circle of radius a, and the other section the diameter joining the two ends of the semicircle. The body is free to move about the midpoint O of its...
  7. O

    The angular speed of precession for a gyroscope is given by

    The angular speed of precession for a gyroscope is given by ω_{p} = T/ω_{g}. So that the rate of precession increases as the gyroscope, top, or wheel slows down. This agrees with observations of a top, which wobbles around very quickly as it slows down. If I hold a bicycle wheel in my...
  8. S

    What is the Angular Speed After Collision?

    Hello, I'm having difficulty with this problem. I'm assuming all the kinetic energy of mass m is transferred to rotational kinetic energy after the collision so 1/2 mv2 = 1/2 I ω2 where I is now Md2/12 + m(d/2)2 =3/4 md2 Solving, ω = 2v/√3d But the answer should be 2v/3d. Thanks!
  9. S

    Angular speed and acceleration of a rod

    Homework Statement A rod with one end fixed on a smooth hinge is shown below. The rod is released from horizontal position so that it rotates at the hinge. The mass of the rod is 800 gr and the length is 120 cm. Find: a. the initial angular acceleration (at A) b. the angular...
  10. P

    What is the angular speed limit, like linear speed limit is c?

    what is the angular speed limit, like linear speed limit is c?? does there exist an angular speed limit, just like we have 'c' in relativistic mechanics? If Yes, How? If No, Why?
  11. K

    Angular Speed Problem: Understanding the Effects of Weight Release on Rotation

    A student is sitting on a frictionless rotating stool with her arms outstretched holding equal heavy weights in each hand. If she suddenly let's go of the weights, her angular speed will: A) increase B) stay the same C) decrease attempt: i think it's B because angular speed is V/r and...
  12. S

    Finding angular speed of a system about its center of mass after the impact

    Homework Statement 1. Homework Statement On a frictionless table, a glob of clay of mass 0.72 kg strikes a bar of mass 1.34 kg perpendicularly at a point 0.23 m from the center of the bar and sticks to it. If the bar is 1.22 m long and the clay is moving at 8.3 m/s before striking the...
  13. M

    Physics Question Involving Angular Speed and Angular Velocity.

    Homework Statement An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the outside edge of the wheel, as in Fig. 10-29, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot...
  14. P

    Robot cinematic model. Which method to get linear and angular speed?

    Hello all! I have a question regarding how to get the linear and angular speed for this robot for example (RRP). http://img205.imageshack.us/img205/774/rrp.png I am given x and y or the hand, as well as theta (angle) If I were asked to calculate the linear. Do I derive x and y to...
  15. S

    Angular Velocity or Angular Speed?

    Hi, We have been studying centripetal forces and accleration in my class, and my teacher has shown me how to derive centripetal acceleration as v^2/r using change in velocity over time. I recently got into angular velocity vs. linear velocity in my math class, and I know that angular...
  16. M

    Calculating satellite's angular speed at perihelion

    Homework Statement A satellite is in elliptical orbit with a period of 8.00 x 10^4 s about a planet of mass 7.00 x 10^24 kg. At aphelion, at radius 4.5 x 10^7 m, the satellite's angular speed is 7.158 x 10^-5 rad/s. What is its angular speed at perihelion? Homework Equations...
  17. M

    How Does Dropping Clay Affect a Potter's Wheel's Angular Speed?

    Homework Statement A potter's wheel, with rotational inertia 6.40 kg * m^2, is spinning freely at 19.0 rpm. The potter drops a 2.80 kg lump of clay onto the wheel, where it sticks a distance of 47.0 cm from the rotation axis.Homework Equations I know I need to use angular momentum here, but I...
  18. lonewolf219

    Angular speed and tangential velocity

    i am wondering if this is correct... The angular speed is always a smaller magnitude than the tangential velocity. This is because the tangential velocity has to travel a larger distance during the same amount of time as the angular speed. Tangential velocity is dependent on two things...
  19. R

    Two rotating disks, angular speed and kinetic energy question.

    Homework Statement A uniform disk of mass 9.00m and radius 2.00r can rotate freely about its fixed center like a merry-go-round. A smaller uniform disk of mass m and radius r lies on top of the larger disk, concentric with it. Initially the two disks rotate together with an angular velocity...
  20. A

    Angular speed vs. Orbital speed

    Homework Statement Consider a year to be precisely 365 days. Determine the angular speed of the Earth about the sun. If the Earth's mean distance from the sun is 1.496x1011 meters and our orbit is circular, determine our orbital speed about the sun. Homework Equations ω=Δθ/T, where ω is...
  21. P

    Rotational Motion angular speed

    Homework Statement 11. A wheel with an angular speed of 2.0 rad/s is rolling on a horizontal surface and starts down a ramp. It rolls down the ramp with a constant angular acceleration of 2.5 rad/s2. If it takes 8 s to reach the bottom of the ramp, what is the final angular speed of the...
  22. I

    What am I doing wrong in this problem dealing with Angular Speed

    Homework Statement For some reason, I keep getting this problem wrong, could someone please look over it and tell me what I am doing incorrectly? Here it is: A student ties a 410.0 g rock to a 1.25 m-long string and swings it around her head in a horizontal circle. At what angular speed (in...
  23. I

    How Do You Calculate the Angular and Linear Speed of a Ball?

    Homework Statement a ball moves at 5000 rpm (revolutions per minute). Their radius is 4 cm. (i)Determine the angular speed in radians per second. (ii) Find the period of rotation (iii) Find the linear speed of a point on the outer ball (iv) Find the linear acceleration of a point on...
  24. D

    Angular speed; horizontal circle

    Homework Statement A student ties a 400g rock to a 1.0m long string and swings it around her head in a horizontal circle. What angular speed does the string tilt down at a 10° angle? m = 400g = .4kg r = 1m Homework Equations F = \frac {mv^2}{r} \omega = \frac {|v|sin \theta}{|r|}...
  25. L

    Show a second angular speed given a reduced radius

    Homework Statement A particle on a string at radius r=0.22m is moving in a (horizontal) circle with angular speed \omega =0.55 rad/s. The string is shortened to 0.15m. Show that the new angular speed is 1.18rad/s Homework Equations v = r\omega a = \omega^{2}r a = r\alpha...
  26. S

    How to calculate torque of a rotating wheel at constant angular speed?

    Suppose there is a rotating wheel at constant angular speed, i.e, 1000 RPM (Revolution Per Minute). What is the torque of Earth at certain location? The equator should have the maximum torque value. I find the angular speed w by 1000 x 2Pi rad x 1 / 60s = 104.71 rad/s Assume M is the mass of...
  27. M

    What Determines the Peak Angular Speed of a Rotating Cylinder?

    Homework Statement In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 1.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as θ =2.50t2 - 0.600t3 where θ is in...
  28. N

    Solving Bacterial Motor Angular Speed and Time for One Revolution

    Homework Statement Some bacteria are propelled by motors that spin hair-like flagella. A typical bacterial motor turning at a constant angular velocity has a radius of 1.8x10-8m, and a tangential speed at the rim of 1.8x10-5 m/s. (a) What is the angular speed (the magnitude of the angular...
  29. N

    Work and Bernoulli Eqn in Rotating Frame with Constant Angular Speed

    Q 1:Consider a disk of radius R. This disk is rotating around its center with a constarnt angular speed of w. Find the necessary work to move a body of mass m radially with respect to the disk from r=a to r=b. Q 2:The Bernoulli equation for a unit mass can be written as gdz+1/2VdV+vdP=0...
  30. L

    Calculating Angular Speed in a Rotating System with Sliding Rings

    A uniform rod of mass 2.95×10−2 kg and length 0.440 m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.240 kg, are mounted so that they can slide along the rod. They are initially held by catches at positions a...
  31. E

    How to Calculate Angular Speed of a Rotating Turntable with Added Mass

    Homework Statement A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00m and a total mass of 140kg . The turntable is initially rotating at 2.00rad/s about a vertical axis through its center. Suddenly, a 65.0-kg parachutist makes a soft landing on the turntable at...
  32. A

    Finding Angular speed and momentum

    Homework Statement The problem: A merry-go-round has a radius of 1.40m and a mass of 125kg. You may consider the merry-go-round to be a solid disk. A 60.0kg student stands on the outer edge of the merry-go-round, 1.40m from the center(the axis of rotation). It takes 3.00s for the...
  33. B

    Angular speed of rotating coil in the Earth's magnetic field

    Homework Statement A circular loop of wire of radius 1.5 cm is mounted in the Earth’s magnetic field, with no other magnetic fields present. It is free to rotate about an east–west horizontal axis which lies along a diameter of the coil. At what angular speed must it be rotated in order for...
  34. R

    What is the angular speed of the insect?

    Homework Statement ok this is a little silly. An apparatus of the figure below is designed to study insects at an acceleration of magnitude 910 m/s2 (= 93g). The apparatus consists of a 2.0-m rod with insect containers at either end. The rod rotates about an axis perpendicular to the rod...
  35. K

    Long string wrapped around cylinder. Find cylinders angular speed?

    Homework Statement A long string is wrapped around a 6.3-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 2.0 m/s2 until 1.5 m of string has been unwound. If the string unwinds without slipping, what is the...
  36. G

    Calculating Final Angular Speed of Rotating Table

    Homework Statement a 40kg duck walks from the outside to the inside of a rotating circular table of mass 100kg. if the rotational intertia of the table is 250kg*m^2 and the duck moves from a radius of 2.5m to 1.5m, find the final angular speed of the table if it rotates at 2.0rad/sec at the...
  37. M

    Proof of angular speed of satellite

    Homework Statement http://img577.imageshack.us/img577/5457/gmblrekp.th.jpg Homework Equations The Attempt at a Solution Proof was asked from me. How do i proof it. In "w^2 sub. uydu", uydu means satellite.
  38. M

    What is the Angular Speed of a Disk Pulled with a Constant Force?

    Homework Statement A 6kg disk with radius 0.3m initially not spinning. String is wrapped around disk, you pull with constant force of 25N through a distance of 0.6m. What is its angular speed. Homework Equations Krotational=1/2 I w2 The Attempt at a Solution I can't seem to...
  39. W

    Falling thin rod and angular speed

    Homework Statement A 1.80 m long thing rod is balanced vertically on its tip on the floor. It starts to fall and its lower end does not slip. What is its angular speed just before it hits the floor? Homework Equations 1/3ML^2 L=mvr The Attempt at a Solution When I first started...
  40. P

    Angular speed at bottom of loop

    Homework Statement A circular ring with a mass of 11 kg and radius of 0.66 meters is to roll without slipping about a vertical loop of radius 10 meters which is frictionless. If it is to just barely make it around the top of the loop, what must its angular speed be at the bottom of the loop...
  41. G

    Circular Motion with Angular Speed dealing with planets

    1. Homework Statement Mars orbits the sun at a mean distance of 228 million km, in a period of 687 days. The Earth orbits at a mean distance of 149.6 million km in a period of 365.26 days. All answers should be in the range (0, 2pi) a) suppose Earth and Mars are positioned such that Earth...
  42. Z

    Angular speed of a disk, given a force

    Homework Statement A uniform-density 7 kg disk of radius 0.27 m is mounted on a nearly frictionless axle. Initially it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 45 N through a distance of 0.9 m. Now what is the angular...
  43. A

    Woman walking around table, find angular speed of table.

    Homework Statement A woman with a mass of 70 Kg stands at the rim of a horizontal table having a moment of inertia of 490 kg*m^2 and a radius of 1.4 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axis through it's center. The woman then starts...
  44. H

    Magnitude of Final Angular Speed of Rolling Sphere

    Homework Statement A block with mass 2 kg is hanging from a string that goes over a solid disk pulley with mass mdisk = 2 kg and radius Rdisk = 0.3 m with tension T1=11.34N between them. The other end of the string is attached to a massless axel through the center of an sphere on a flat...
  45. S

    Calculating Angular Speed for a Gravitational Field of 1.95g

    Homework Statement A biologist studying plant growth and wants to stimulate a gravitational field stronger than the Earth's. She places the plants on a horizontal rotating table in her laboratory (on Earth) at a distance of 42.3 cm from the axis of rotation. What angular speed will give the...
  46. M

    Use conservation of energy to determine the angular speed of a spool

    Homework Statement Use conservation of energy to determine the angular speed of a spool after the bucket(3.0kg) has fallen 4.00m, starting from rest. Homework Equations KE = 1/2mv^2 KEr = 1/2 * I * omega^2 PE - mgh The Attempt at a Solution i don't know how to start. I...
  47. R

    What is the Average Angular Speed of the Leaning Tower of Pisa?

    Homework Statement The top of a tower much like the leaning bell tower at Pisa, Italy, moves toward the south at an average rate of 1.4 mm/y. The tower is 59 m tall. In radians per second, what is the average angular speed of the tower's top about its base? Homework Equations...
  48. B

    Perfectly Inelastic Disk and Stick Collision- Angular Speed

    I think I'm not understanding something about this problem. Can someone help me out? Homework Statement A 2.0 kg disk traveling a 3.0 m/s strikes a 1.0 kg stick of length 4.0 m that is lying flat on nearly frictionless ice. The disk strikes the endpoint of the stick, at a distance r = 2.0 m...
  49. M

    Calculating Angular Speed After Spoke Shortening in Rotating System

    Homework Statement The system of small objects shown in the figure below is rotating at an angular speed of 2.0 rev/s. The objects are connected by light, flexible spokes that can be lengthened or shortened. What is the new angular speed if the spokes are shortened to 0.10 m? (An effect...
  50. M

    Angular Speed Homework: Car Brakes, Radii & Revs

    Homework Statement A car initially traveling at 33.8 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after 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...
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