# 0.29 Phy1260: circular motion -- the mathematics of circular motion  (Page 3/7)

 Page 3 / 7

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

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.

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

where

• 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

what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
Jeannette has \$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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