Question

Angular and linear speed….

A cyclist is riding a bicycle whose wheels have a radius of
10
inches. Suppose he is traveling at
22
miles per hour. (A useful fact:
=1mi5280ft
.)
(a) Find the angular speed of the wheels in radians per minute.
(b) Find the number of revolutions the wheels make per minute.

Do not round any intermediate computations, and round your answer to the nearest whole number.

Answer 1

what do you have so far?

Answer 2

nothing yet… I'm not to sure how to start.

Answer 3

so the radius is 10 inches?

and the speed is 22 mph?

or are any values given as fractions or something?

Answer 4

yes and yes… and no

Answer 5

Given the radius r = 10, what is the circumference of the bike wheel?

Answer 6

idk

Answer 7

you would use the formula

C = 2*pi*r

C is the circumference
pi is approximately 3.14
r is the radius

Answer 8

so 20pi

Answer 9

very good

Answer 10

thanks

Answer 11

the units for the circumference is in inches

Answer 12

so now what?

Answer 13

the speed is 22 miles per hour

we have inches for the wheel but miles for the speed, so we first have to convert from miles to inches

( 22 miles ) * ( 5280 ft/1 mile) = 22*5280 = 116,160 feet

(116,160 feet) * (12 inches/1 ft) = 116,160*12 = 1,393,920 inches

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

So we now know that

22 miles = 1,393,920 inches

making sense so far?

Answer 14

yes but my computer in gonna die and i don't have my charger.

Answer 15

how much time do you have?

Answer 16

if not a lot, then I can come back later

Answer 17

its at 2%

Answer 18

its is making sense though

Answer 19

anyways,

22 mph = 1,393,920 inches per hour

we need to go from inches to hour to inches per min

so we multiply by (1 hr/60 min)


(1,393,920 inches/1 hr)*(1 hr/60 min) = 1,393,920/60 = 23,232 inches per min

Answer 20

it's a lot of steps, but we now know

22 mph = 23,232 inches per min

Answer 21

ok

Answer 22

One full revolution corresponds to the circumference C

so we can say

1 rev = 1 C

which is the same as

1 rev = 20pi inches

we now take our last result (23,232 inches per min) and multiply it by (1 rev/20pi inches)

to get...

(23,232 inches/1 min)*(1 rev/20pi inches) = 23,232/20 = 1,161.6

this means that the angular speed is 1,161.6 revolutions per min

convert (1,161.6 rev/1 min) to rad/min

(1,161.6 rev/1 min)*(2pi rad/1 rev) = 1,161.6*2pi = 2,323.2pi rad/min

Answer 23

so the angular speed is 2,323.2 radians per min

Answer 24

ok i understand that…

Answer 25

sorry I had to log off, but I'm back

Answer 26

were you able to answer the second part?

Answer 27

thats fine no worries no i wasn't able to. :(

Answer 28

Notice how in my steps I had "1,161.6 rev/1 min". It's towards the end.

so it makes 1,161.6 revolutions in 1 minute