Thread: Some word problems. Please help!

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.

Thank you all in advance!

Do you have any attempts of finding solutions to supplement these questions?

Have you researched which formulas may help?

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

answer wasnt correct.

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

answer wasnt correct.

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

Originally Posted by niCe99

i simply converted the pi into 120/360 (since pi = 360)

Not sure who told you that!

Try,

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

would give you the linear speed in m/sec.

Originally Posted by pickslides

Not sure who told you that!

Try,

Amazing!

thank you so much

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

would give you the linear speed in m/sec.

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

thanks

Originally Posted by niCe99

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

thanks

the basic formula for linear speed is , where is the linear speed in m/s and is the angular speed in rad/sec

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:

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:

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.

oh is that why you would multiple 5m/1rad with 220rad/sec? since we have the radian...

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.

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

... and to convert from radians to degrees, multiply by
.

oh is that why you would multiple 5m/1rad with 220rad/sec? since we have the radian...

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: .)

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.)

appriciate the answer!

yeah, my courses/school is weird. i took all of the pre-req math courses but they never taught any trig whatsoever. the last pre-calc class i took was more theory base (intermediate value therom and basic graphs/hows to graph/ "advanced" algebra) but no where did i learn trig.

The next class i took was a split of Calculus 1 where i only studied the derivatives of polynomials/radicals/power functions and ect with the exclusion of trigonometry and logarithms. I did very well in that class but the second half where it is trig, is really kicking me in the butt. My midterm is compose of half trigonometry related problems (identities, problem solving such as the above and inverse/graphing) while the other half is calculus with trig, related rates/derivatives/linearizion.

regardless, thank you for the help!