Question

A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular speed of the wheels in radians per minute. ___ radians per minute
How many revolutions per minute do the wheels make? (Round your answer to three decimal places.) ___ revolutions per minute

Answer 1

Answer:

a) 2211.6812281 rad/min

b) 352 rpm

Step-by-step explanation:

A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular speed of the wheels in radians per minute. ___ radians per minute

How many revolutions per minute do the wheels make? (Round your answer to three decimal places.) ___ revolutions per minute

truck with 24-in.-diameter wheels is traveling at 16 mi/h.

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1 mile per hour = 88 feet per minute

16 mi/hr = 1408ft/minute

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Each revolution = pi*d feet = 4pi feet

(b) How many revolutions per minute do the wheels make?

rev/min

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Each revolution = pi*d feet = 4pi feet

rpm = 1408 ft/min / 4pi feet

=~ 352 rpm

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(a) Find the angular speed of the wheels in rad/min.

rad/min

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rad/min = rpm*2*pi

= 352 rpm × 2× π

= 2211.6812281 rad/min

Answer 2

So, the wheels make $224.20 \ rev/min$.

Angular Sped:

Angular speed measures how fast the central angle of a rotating body changes with respect to time. It is expressed as,

$\omega=\frac{\theta}{t}$

Given that:

Diameter$=24 \ in$

Radius$=12 \ in$

First, we have to find the angular speed($\omega$):

We use the formula,

$v=\omega r$

Substituting,

$16 \ mi/hr=\omega \times 12 \ in$   ($\therefore$ $1mile=63360inches, \ and \ 1hour=60min$)

$=\frac{16 \ mi\times \left ( 63360 \ in/mi \right )}{\left ( 1 \ hr\times 60 \ min/hr \right )}$

$=\omega \times 12 \ in$

$\Rightarrow 15840 \ in/min=\omega \times 12 \ in$

$\omega =16896/12\\w=1408 \ rad/min$

Now, we have to find rev/min:

($\therefore \ 1 \ revolution=2\pi$)

Thus,

$1408 \ rad/min\times1 \ rev/2\pi \ rad=224.20 \ rev/min$..

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