# What is Rotational velocity: Definition and 30 Discussions

In physics, angular velocity or rotational velocity (

ω

{\displaystyle {\boldsymbol {\omega }}}
or

Ω

{\displaystyle {\boldsymbol {\Omega }}}
), also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
There are two types of angular velocity. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular velocity.
In general, angular velocity has dimension of angle per unit time (angle replacing distance from linear velocity with time in common). The SI unit of angular velocity is radians per second, with the radian being a dimensionless quantity, thus the SI units of angular velocity may be listed as s−1. Angular velocity is usually represented by the symbol omega (ω, sometimes Ω). By convention, positive angular velocity indicates counter-clockwise rotation, while negative is clockwise.
For example, a geostationary satellite completes one orbit per day above the equator, or 360 degrees per 24 hours, and has angular velocity ω = (360°)/(24 h) = 15°/h, or (2π rad)/(24 h) ≈ 0.26 rad/h. If angle is measured in radians, the linear velocity is the radius times the angular velocity,

v
=
r
ω

{\displaystyle v=r\omega }
. With orbital radius 42,000 km from the earth's center, the satellite's speed through space is thus v = 42,000 km × 0.26/h ≈ 11,000 km/h. The angular velocity is positive since the satellite travels eastward with the Earth's rotation (counter-clockwise from above the north pole.)
Angular velocity is a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves, and its direction pointing perpendicular to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.

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1. ### Translational and rotational velocity

For a cylinder rolling down an inclined plane, does the tangential velocity of a point a distance R from the axis of rotation equal the velocity of the center of mass?
2. ### What was the rotational velocity of Earth on Dec 31, 1899

I ask because time is defined with reference to this day (the SI second is based on a caesium clock is calibrated with reference to the 1952 ephemeris time standard, which was based on a second being 1/86 400th of Jan 0, 1900 (with Jan 0 being Dec 31 of 1899). So... how do I calculate the...
3. ### What is the rotational velocity of hard disk actuator arm?

0 down vote favorite There is a lot of material discussing the rotational speed of the magnetic disk in HDD but not about the rotational speed of actuator arm. What are the typical actuation speeds of the actuator in HDD? This information will be used in the design of a fast shutter system...
4. ### Rotational velocity of the ring

Homework Statement Homework EquationsThe Attempt at a Solution Wrt inertial frame with origin at the pivot, [/B] The final angular velocity of the ring, the bug are ## \vec ω_r ## and ## \vec ω_b ## and the final velocity of the bug is ## \vec v_b ##. Since, there is no net external...
5. ### Power Output Given Certain Torque

Hi, I have a problem that I've been trying to figure out for a while but cannot seem to get on my own. I'm trying to figure out how much power will be generated in a motor given a certain amount of torque. The problem is, to find the amount of power output , I also need to know the rotational...
6. ### Rotational Velocity with 2 Gears

Homework Statement A small gear with mass m and radius r rotate around a central axis. A force is applied to an interior hub at a radial distance r/2 from the axis. A. If a force of 4N is applied for 10s, what is the angular velocity of the small gear, assuming it starts at rest? B. Once it...
7. ### What is the rotational velocity of the crank?

Homework Statement You accidentally knock a full bucket of water off the side of the well. The bucket plunges 13 m to the bottom of the well. Attached to the bucket is a light rope that is wrapped around the crank cylinder. The cylinder has a radius of 0.085 m and inertia of 4.0 kg. The inertia...
8. ### Need animation/video to convey rotational speeds

Hello Everyone, I need an animation or video or something that will convey different speeds of different sized circles. Ideally, I would like some type of tire setup that shows a smaller circle driven at the same speed rotating more quickly than a larger circle. I am using this for an...
9. ### Earth's Rotational Velocity: Find Linear Velocity

Homework Statement Find the linear (or tangential) velocity of a point on the Earth's equator in the frame of reference about a stationary rotational axis as it spins over the course of one day. Homework EquationsThe Attempt at a Solution I do not understand what the frame of reference is?? If...
10. ### Does driving a car affect the Earth's rotational velocity

hi guys really odd question (no such things as a silly question) but i was just thinking about this and well according to Newtons every action has an equal and opposite reaction well i know I am talking fractions of a degree per millenia or there abouts i guess but when i get in my car with a...
11. ### Combining translational and rotational velocities to get rotational velocity

Homework Statement Suppose you are standing uptight with your right arm stretched out straight in front of you, palm down, the upper arm rotating rightward relative to space at 2 radians/s and the elbow flexing in the horizontal plane at 2 radians/s. What is the rotational velocity of the...
12. ### Rotational Velocity and Acceleration

1. Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.1 cm in diameter that rotates back and forth through a 70.0 angle 7600 times per minute. The rim of the head contains a thin row of bristles. (See the figure )Assuming that the toothbrush has...
13. ### Orbital velocity and rotational velocity

Hi Is "orbital velocity" supposed to be the same as "rotational velocity"? it seems that a "rotation curve" is supposed to plot the rotational velocity of a star, but then some articles e.g. http://en.wikipedia.org/wiki/Galaxy_rotation_problem claim "orbital speed" is plotted. The equation...
14. ### Equation relating rotational velocity and output electrical power

What is the equation that relates the angular velocity of an alternator rotor with its output electrical power, voltage and frequency (not necessarily just one equation) . And for a DC generator? I know that when you calculate the power generated by a turbine you multiply its efficiency of...
15. ### Advanced Rotational Velocity Question

Homework Statement A particle of mass m rotates with a uniform speed on the inside of a bowl's parabolic frictionless surface in a horizontal circle of radius R=0.4 meters as shown below. At the position of the particle the surface makes an angle θ=20 degrees with the vertical. The angular...
16. ### Comparing Angular Rates of Star Rotation at Different Latitudes and Longitudes

The Earth's rotational velocity at the Equator is 1,674.4 km/h or 465.1 m/s. The stars at the equator rotate at that same rate taking in account Precession at that particular time of the year and the longitude & latitude they are viewed from. Do the stars at the poles rotate faster then at the...
17. ### Rotational Kinetic Energy Problem

Homework Statement A thin uniform-density rod whose mass is 3.8 kg and whose length is 3.0 m rotates around an axis perpendicular to the rod, with angular speed 34 radians/s. Its center moves with a speed of 10 m/s. (a) What is its rotational kinetic energy? (b) What is its total kinetic...
18. ### Ratio of translational velocity to rotational velocity.

1. A ball of mass m and radius R is both sliding and spinning on a horizontal surface so that its rotational kinetic energy equals its translational kinetic energy.What is the ratio of the ball’s center-of-mass speed to the speed due to rotation only of a point on the ball’s surface? The moment...
19. ### Bug on a pivoted ring: rotational velocity

Homework Statement Hi guys, this question is from Kleppner and Kolenkow, problem 6.3. A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the...
20. ### Rotational Velocity Homework: Find Accel & Distance for Stopping Wheel

Homework Statement A wheel has a rotational velocity of 14 rad/s clockwise you place your hand against the wheel and the friction between your hand and the rim stops it a) If it takes 5s to stop the wheel what is its rotational acceleration b)How far does the wheel rotate while slowing to a...
21. ### Torque <-> rotational velocity?

Hello. I'm having a bit of a problem. I need to calculate a change in rotational velocity on a rigid object given a force (actually an impulse, but nevermind) acting on that object. I can calculate the torque without problem, by doing the cross product of the force vector and the offset...
22. ### Rotational Velocity Question - I think?

It has been said that a parade of Chinese twenty a breast could march forever past an observing point. If we assume the parade to march at 3 miles per hour, with ranks 4 feet apart, what is the Chinese birth rate, in babies per hour? ok, so far I've drawn a picture, and converted all my...
23. ### Rotational velocity of a system that has a mass launched at it stick to it

Homework Statement On a frictionless table, a glob of clay of mass 0.74 kg strikes a bar of mass 1.90 kg perpendicularly at a point 0.48 m from the center of the bar and sticks to it. If the bar is 1.50 m long and the clay is moving at 6.8 m/s before striking the bar, at what angular speed...
24. ### Measuring the earths Rotational velocity

Homework Statement Brief: Using the following: 1 ruler or stick, 1 tape measure, 1 ball of string, 1 timer, 1 calculator (+anything else you think you need) Create an experiment which you will measure the rotational velocity of the earth. Initially what you must do is measure the time it...
25. ### Rotational velocity of a planet

I was thinking, the amount of "gravity" a person feels on the surface of a planet is not only dependent on gravity, but also the centripetal force... For example, if Earth spun 17.04 times as fast as it does now (i.e. 1 day = 1.4 hours) then anything on the surface of the Earth would...
26. ### Calculating Rotational Velocity and Force on a Loop-the-Loop Track

I have been trying this question for so long and I still cannot figure out how to do it... A solid brass ball of mass 8.2 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 4.9 m, and the ball has radius r <<...
27. ### Analog Signal Meters for Rotational Velocity & Angle Measurement

Is there any kind of signal meter that can take an analog output of rotational velocity, angle etc. and show it in its full form. If there is meters like this could you recommend a few? Thanks
28. ### Pivots and rotational velocity

I'm trying to work out the science of a simplified model of the human body, and I would appreciate your help on some of the basic formulae. If I have a bar (representing the shoulders), which has a central pivot point, connected by a unrestricted hinge to a rod (representing the upper arm...
29. ### Rotational velocity and the speed of light

We all know that, as an object rotates about an axis in constant circular motion (\omega is constant), the linear velocity increases the further the object is from the axis (v increases as r increases, v = \omega * r) Let's say you build a scyscraper. The taller the skyscraper, the faster...
30. ### Calculate Rotational Velocity of Object Around Fixed Point

How could i calculate the velocity of an object rotated around a fixed point such as a hand on a clock. It seems as though each section of the hand would have a different velocity, the end part being the fastest while the beginning part being the slowest if not moving at all. I am guessing the...