Trig Confusion?

Question

So I wouldn't be asking this question if I hadn't already tried forever to figure it out on my own.... so........ please..... help. lol

...This should be really easy, but I think I'm missing something somewhere......

Here's the problem:

Angular Speed - A Car is moving at a rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet

(a) Find the rotational speed of the wheels in revolutions per minute.

(b) Find the angular speed of the wheels in radians per minute.

PLEASE help. I've done this problem in so many ways, and I keep getting different answers that do NOT make sence. And I need an explanation... not just an answer.....

It should come out to

(a) 560.2 revolutions per minute and (b) 3520 radians per minute.

But I don't know how to get to those answers....



Thanks in advance.

Answer 1

convert to feet per minute first:
50 miles divided by 60 minutes for miles per minute
take the miles per minute and multiply by 5280 ft to get feet per minute which equal 4400

Now find the circumference of the wheel:
circumference = 2.5 x pi(3.141592654)-------
circumference = diameter x pi
2.5 x 3.141592654 = 7.85398 ft

to find revolutions per minute:

feet per minute (4400) divided by the wheels circumference (7.85398 ft)

and it equals 560.2255162, which when rounded to one decimal place would be 560.2

To find revolution per minute in radians:

Take the number of revolutions per minute (560.2255162) x 2pi since there are 2pi radian in a revolution

560.2255162x 2(3.141592654) which equals 3520.00063, which rounds to 3520

Answer 2

Circumference of the wheel is Pi * D so in feet it is:
2.5 * 3.14159 = 7.853975 ft
Speed forward of the car in feet per minute (since you want to talk about revolutions per minute) is: 50 mph * 5280 ft/mi /60 min/hr or 4400 ft/min
Assuming the tire does not slip on the pavement, in the 1 minute the car moves forward, the tire rim (circumf) must cover the same distance. So for every 7.853875 ft, the tire makes 1 rev. By division, 4400/7.853975 = 560.22
There are 2Pi radians in a complete circle so in 1 rev the tire covers 2 *3.14159 rad. Multiply the RPMs by 2 Pi
560.22*2*3.14159 = 3520 rad/min

Answer 3

The speed of the car is the same as the speed of the edge of the wheel. In one rotation the wheel covers pi*d feet. in 50 miles there are 50*5280 feet. Divide this by pi*d to get the number of tuns in one hour. Divide again by 60 to get turn (revolutions) per minute.

One revolution contains 2*pi radians. Multiply RPM by 2*pi to get rad/min

Answer 4

v * t = w * O (angular velocity times degrees/ radians/ revolutions)

50 miles / hour = 50 * 5280 ft / 60min = 4400 ft/min

1 revolution is how many feet? C = pi * d = pi*2.5 ~= 7.854

4400 ft/ min / 7.854 = 560.22 rev/min


Once you've got revs/min, radians/min should be easier!

560.22 rev/min *(2 pi radians / 1 rev) ~= 3520 rad/min
{since there are 2pi radians in 1 revolution.}

I hope this helped! Send me a message if you want more explanation!

Answer 5

speed of the car = speed of the periphery of the wheels = speed.
speed = angular speed x radius
50 miles/hour = angular speed x 2.5 feet
(50 x 5 280) feet / 60 min = angular speed x 2.5 feet
angular speed = 11 x 10^5 rad/min = answer b.


angular speed = 2pi / period
1 /period = 2pi / angular speed = 17 x 10^3 rotations/min = answer a.

Th

Answer 6

C = pi * 2.5
C = 2.5pi
C = (5/2)pi
C = (5pi)/2 ft

50 miles = 5280 * 50 = 264000

1 hour = 60 minutes

264000/60 = 4400 ft/min

4400/((5pi)/2) = (4400/1)/((5pi)/2) = (4400/1)*(2/(5pi)) = (8800/5)(1/pi) = 1760/pi = about 560.2 revolutions per minute

Just take the miles, put them in ft, then divide them by the circumference of the tires. The wheels would travel (5pi)/2 ft, so 264000/(5pi/2) = 33613.52 revolutions per hour, divide that by 60 and you would get 560.2 revolutions per minute.

-----------------------------------------------------------------------

(5pi/2)/(2pi) = (5pi/2)/(2pi/1) = (5pi/2)*(1/(2pi)) = (5pi)/(4pi) = (5/4)

264000/(5/4) = (264000/1)/(5/4) = (264000/1)*(4/5) = (1056000/5) = 211200 radians per hour

211200/60 = 3520 radians per minute

all your doing is taking the distance and dividing it by the diameter, then dividing that by 60.

Answer 7

Tangent 32=x/22.......tan32 on your calculator supplies you you with a extensive variety. Set that extensive variety resembling x/22, and treatment for x. i'm going to faux the project is tan7 = x/2just to coach you the stairs. tan7 = .12......12/a million = x/22...flow multiply and you have (.12)(22) = x; x = 2.sixty 4 basically stick to the comparable steps to treatment your project tangent 27=x/12 comparable steps as above tangent y= 2n/n.....simplify 2n/n...do now no longer the n's cancel? tany = 2 remember, in an inverse, the sport enthusiasts substitute places. If tany = 2, Then tan inverse(2) = y frequently you press you 2ndf key and tan^-a million(2) on your calculator stable success! digital mail w/ questions

Answer 8

2.5 ft * 3.14 = 7.85 ft per second for a point on the rim of the wheel
50 mph = 264 000 feet per hour or 4400 feet per second
4400 / 7.85 = 560.5 revs per second

Answer 9

You need to include "Surface Feet" in your work,then it will all make
sense.