SOLUTION: I have a test tomorrow and for some reason i just can't understand these problems!! Please help! A car is moving at a rate of 28 miles per hour, and the diameter of its wheel i

Question 914718: I have a test tomorrow and for some reason i just can't understand these problems!! Please help!
A car is moving at a rate of 28 miles per hour, and the diameter of its wheel is about 2 1/3 feet.
A.) find the number of revolutions per minute the wheels are rotating.
B.) find the angular speed of the wheels in radians per minute.

Found 3 solutions by jim_thompson5910, Alan3354, LinnW:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Throughout this problem, I will use the constant pi. That is approximately equal to 3.14; however, you can use a more accurate approximation (say pi = 3.1416) to get a more accurate answer.

Also, even if you ignore pi and its approximations, there will be rounding errors that accumulate. So keep this in mind.

A)

The diameter of the wheel is 2 1/3 ft. So d = 2 + 1/3

Circumference

C = pi*d

C = 3.14*(2 + 1/3)

C = 7.326667

The circumference is roughly 7.32666 feet.
-------------------------------------------------------

Convert 7.32666 feet to miles

(7.32666 feet)*(1 mile/5280 feet) = 7.32666/5280 = 0.001387625 miles

7.32666 feet = 0.001387625 miles (approximate)

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

(28 miles/1 hour)*(1 revolution/0.001387625 miles) = 28/0.001387625 = 20,178.3623097019 revolutions per hour

Now convert from "revolutions per hour" to "revolutions per minute"

(20,178.3623097019 rev/1 hour)*(1 hour/60 minutes) = 20,178.3623097019/60 = 336.306038495031

The final answer for part A) is 336.306038495031 revolutions per minute (this is approximate).

=============================================================================
B)

Take the answer from part A) and multiply it by the conversion factor (2 pi radians/1 rev) to convert to "radians per minute"

This works because 2pi radians = 1 revolution

(336.306038495031 rev/1 minute)*(2pi radians/1 rev) = 336.306038495031*2pi = 336.306038495031*2*3.14 = 2,112.0019217488

So the angular speed is roughly 2,112.0019217488 radians per minute

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A car is moving at a rate of 28 miles per hour, and the diameter of its wheel is about 2 1/3 feet.
A.) find the number of revolutions per minute the wheels are rotating.
B.) find the angular speed of the wheels in radians per minute.
------------------
Find the circumference of the wheel.
C = pi*d = 8pi/3 feet
The car moves 8pi/3 ft per revolution (assuming no slippage or burning of rubber)
---
Convert mi/hr to ft/sec
15 mi/hr = 22 ft/sec
28 mi/hr = 28*15/22 = 210/11 ft/sec =~ 19 ft/sec
---
rev/sec = 19 ft/sec / 8pi/3 ft/rev
rev/sec = 57/8
rpm = rev/min = (57/8)*60 = 427.5 rpm
-----
radians/min = 2pi*rev/min
=~ 2686.06 rad/min

Answer by LinnW(1048)   (Show Source): You can put this solution on YOUR website!
A.) find the number of revolutions per minute the wheels are rotating.
For this question, convert miles per hour feet per minute.
SO =
=

If we divide 2464 by 2 1/3 we will have the number of revolutions.
2464 by (2 1/3) =

7278/7 = 1039.71 revolutions
One revolution per minute = 6.283 radians per minute
So 1039.71*6.283 = 6532.5 radians per minute

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