# Angles  (Page 9/29)

 Page 9 / 29

A satellite is rotating around Earth at 0.25 radians per hour at an altitude of 242 km above Earth. If the radius of Earth is 6378 kilometers, find the linear speed of the satellite in kilometers per hour.

1655 kilometers per hour

## Key equations

 arc length $s=r\theta$ area of a sector $A=\frac{1}{2}\theta {r}^{2}$ angular speed $\omega =\frac{\theta }{t}$ linear speed $v=\frac{s}{t}$ linear speed related to angular speed $v=r\omega$

## Key concepts

• An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.
• An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x -axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
• To draw an angle in standard position, draw the initial side along the positive x -axis and then place the terminal side according to the fraction of a full rotation the angle represents. See [link] .
• In addition to degrees, the measure of an angle can be described in radians. See [link] .
• To convert between degrees and radians, use the proportion $\text{\hspace{0.17em}}\frac{\theta }{180}=\frac{{\theta }^{R}}{\pi }.$ See [link] and [link] .
• Two angles that have the same terminal side are called coterminal angles.
• We can find coterminal angles by adding or subtracting 360° or $\text{\hspace{0.17em}}2\pi .\text{\hspace{0.17em}}$ See [link] and [link] .
• Coterminal angles can be found using radians just as they are for degrees. See [link] .
• The length of a circular arc is a fraction of the circumference of the entire circle. See [link] .
• The area of sector is a fraction of the area of the entire circle. See [link] .
• An object moving in a circular path has both linear and angular speed.
• The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time. See [link] .
• The linear speed of an object traveling along a circular path is the distance it travels in a unit of time. See [link] .

## Verbal

Draw an angle in standard position. Label the vertex, initial side, and terminal side.

Explain why there are an infinite number of angles that are coterminal to a certain angle.

State what a positive or negative angle signifies, and explain how to draw each.

Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

Explain the differences between linear speed and angular speed when describing motion along a circular path.

Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!