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Reduce the time interval

If we allow the time interval dT to be come shorter and shorter, we are averaging over smaller and smaller time intervals. In the limit, as dTapproaches zero, wAvg becomes w, which is the instantaneous angular velocity.

Angular velocity is a signed quantity

Angular velocity is also a signed quantity with the sign indicating the direction of rotation. By convention, counter clockwise rotation is viewed aspositive rotation. The sign of angular velocity is the same as the sign of the angular displacement that forms the basis for the angular velocity.

Units of angular velocity

The units of angular velocity are typically degrees per second or radians per second. You will learn later that radians is a dimensionless quantity.Therefore, when angular velocity is measured in radians per second, it often appears simply as

w = 10/sec

Radian measure

The most familiar measurement of angles, in the U.S. is in degrees. However, in some situations, it is more convenient to measure angles in radiansthan in degrees.

This becomes most apparent when we need to relate angular displacement or angular velocity with the distance traveled or the tangential speed of a point ona rotating object.

Definition of a radian

One radian is an angular measurement, which is equal to an angle at the center of a circle whose arc is equal in length to the radiusof the circle.

Simulate with a graph board

I recommend that you use your graph board to simulate an angle of one radian.

Using your graph board along with some string and pushpins, draw a Cartesian coordinate system. Then draw a circle with a convenient radius withits center at the origin of your coordinate system.

Make the arc match the radius

Cut a piece of string to the length of the radius of the circle. Then, beginning at the intersection of the circle and the horizontal axis, lay thestring along the circumference of the circle moving in a counter clockwise direction. Put a pushpin at the point where the string ends. Then stretch arubber band from that point back to the center of the circle.

Measure the angle

Using your protractor, measure the angle that the rubber band makes with the horizontal axis. That angle should be about 57.3 degrees, which is one radian.

Measure the number of radians in 360 degrees

Now, using the string whose length is equal to the radius of the circle as a measuring tool, determine how many strings of that length you can lay end-to-endaround the circumference of the circle.

You should find that about 6.28 (2*pi) such strings are required to go all the way around the circumference of thecircle.

An angle in radians is a ratio of lengths

An angle measured in radians is a ratio of two values, each of which have units of length. Therefore, such an angle has no dimensions.

Measurement of an angle in radians

angle = s/r


  • s is the length of an arc along the circumference of a circle
  • r is the radius of the circle
  • angle is the angle subtended by the arc length, s

An example measurement

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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