• Jul 20th 2010, 08:00 PM
niCe99
Hi there, first post on these forums. So i require assistance for a couple of word problems and would greatly appreciate the help.

1)
A wheel is spinning at a rate of 220 rad/sec. Find the linear speed of a point on the rim, if the wheel's diameter is 1.5 meters.

2)
For a circle of radius 30 meters, find the area (to the nearest m^2) of a sector with a central angle of 120degrees.

3)
A flower garden is a 270degree sector with a radius of 4 meters. Find the exact area of the garden (in terms of pi), and approximate to 1 decimal place.

• Jul 20th 2010, 08:17 PM
pickslides
Do you have any attempts of finding solutions to supplement these questions?

Have you researched which formulas may help?
• Jul 20th 2010, 08:23 PM
niCe99
for question number 2, area of a circle is piR^2. by that, i simply converted the pi into 120/360 (since pi = 360) and then proceeded to find the area with the following equation:
120/360 x 30^2

For question 3, i converted 270deg into radians....3pi/2
by the same formula as above....piR^2, i did the following:
3pi/2 x 1/pi x 4^2

question one, i had no idea how to do it. Velocity is m/s but i have no idea how to cancel out the rad
• Jul 20th 2010, 09:07 PM
pickslides
Quote:

Originally Posted by niCe99
i simply converted the pi into 120/360 (since pi = 360)

Not sure who told you that!

Try, $A_{sector} =\frac{\theta}{360}\times \pi r^2 = \frac{120}{360}\times \pi \times 30^2$
• Jul 20th 2010, 09:45 PM
eumyang
Quote:

Originally Posted by niCe99
1)
A wheel is spinning at a rate of 220 rad/sec. Find the linear speed of a point on the rim, if the wheel's diameter is 1.5 meters.

The wheel's radius is 0.75 m, which means that the length of the intersected arc for an angle of 1 radian is 0.75 m. So
$\frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{0.75 \,\text{m}}{1 \,\text{rad}}$
would give you the linear speed in m/sec.
• Jul 21st 2010, 06:38 AM
niCe99
Quote:

Originally Posted by pickslides
Not sure who told you that!

Try, $A_{sector} =\frac{\theta}{360}\times \pi r^2 = \frac{120}{360}\times \pi \times 30^2$

Amazing!

thank you so much :)
• Jul 21st 2010, 06:39 AM
niCe99
Quote:

Originally Posted by eumyang
The wheel's radius is 0.75 m, which means that the length of the intersected arc for an angle of 1 radian is 0.75 m. So
$\frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{0.75 \,\text{m}}{1 \,\text{rad}}$
would give you the linear speed in m/sec.

so 1 rad is proportional to the radius of the circle? always?

thanks
• Jul 21st 2010, 06:44 AM
skeeter
Quote:

Originally Posted by niCe99
so 1 rad is proportional to the radius of the circle? always?

thanks

the basic formula for linear speed is $v = r\omega$ , where $v$ is the linear speed in m/s and $\omega$ is the angular speed in rad/sec
• Jul 21st 2010, 06:47 AM
eumyang
A radian is an angle measure such that if you look at the intercepting arc on the circle, that length would be the same length as the radius. So in the problem, the wheel's radius was 5 m instead, you would set up the multiplication like this:
$\frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{5 \,\text{m}}{1 \,\text{rad}}$
• Jul 21st 2010, 06:56 AM
niCe99
Quote:

Originally Posted by eumyang
A radian is an angle measure such that if you look at the intercepting arc on the circle, that length would be the same length as the radius. So in the problem, the wheel's radius was 5 m instead, you would set up the multiplication like this:
$\frac{220 \,\text{rad}}{1 \,\text{sec}} \times \frac{5 \,\text{m}}{1 \,\text{rad}}$

how does traditional radians, such as pi/2, pi/3, pi/4 ect, in the unit circle get classified? the radius of a unit circle is 1 so....would it just be 1 x whatever radian it is?....so like 1 x pi/3.

sorry. i have NEVER taken a trigonometry class before (they didnt teach it in high school for some reason) and i am doing first year calc and getting my butt kicked from the trigonometry portion of it. In essence, i have had about 8 hours (2 weeks) worth of trigonometry lessons. I learned the basic sin, cos, tan as well as identities and very very vague amount on the unit circles of radians (for what its worth, my teacher is not doing a very good job at teaching trig even though he said he would teach it to us as if we have never seen trig before. I had to self-learn myself but am limited to the resources and TIME, other courses, that i have). We are already up to the calculus portion of trig and thats seems to be alot easier for me anyways.
• Jul 21st 2010, 07:51 AM
eumyang
Quote:

Originally Posted by niCe99
how does traditional radians, such as pi/2, pi/3, pi/4 ect, in the unit circle get classified? the radius of a unit circle is 1 so....would it just be 1 x whatever radian it is?....so like 1 x pi/3.

The formula to find the circumference of a circle with radius r is 2πr, so a circle with radius of 1 m would have a circumference of 2π m. And it's 360° around the circle, so you have the relationship that 360° = 2π rad. Half way around the circle is 180°, and half of 2π rad is π rad. So 180° = π rad.

To convert an angle measurement from degrees to radians multiply by
$\frac{\pi \,\text{rad}}{180^{o}}$
... and to convert from radians to degrees, multiply by
$\frac{180^{o}}{\pi \,\text{rad}}$.

Quote:

That was just a variation of the original problem of converting from angular speed (rad/sec) to linear speed (m/sec), using a different wheel. (BTW I was actually using the formula that skeeter mentioned: $v = r\omega$.)

Quote:

sorry. i have NEVER taken a trigonometry class before (they didnt teach it in high school for some reason) and i am doing first year calc and getting my butt kicked from the trigonometry portion of it.
I'm surprised that you were allowed to take calculus at all! In most course descriptions I've seen trig was a prerequisite. Unless this class is a combination of Calc I and Precalc? (There are classes like this that exist - a year-long class integrating precalculus topics with calculus I.)
• Jul 21st 2010, 08:21 AM
niCe99