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TEA [102]
3 years ago
13

A point on the rim of a wheel moves with a velocity of 60 feet per second. Find the angular velocity of the point if the diamete

r of the wheel is 6 feet. 10 rad/sec 20 rad/sec 180 rad/sec 360 rad/sec
Mathematics
2 answers:
mixer [17]3 years ago
8 0

Answer:

20 \frac{rad }{sec}

Step-by-step explanation:

Hello.

let's see this way.

if you know the distance(a circumference 2πr) and the speed(60 ftps) you are able to find the time it takes a whole spin( a circle)

Step 1

find the distance and time

Let

V=60 \frac{feet}{sec} \\distance= circumference= 2*\pi *r\\diameter=6 feet\\radius=\frac{Diameter}{2}\ so,r=\frac{6}{2} =3 feet\\Hence\\\\distance= circumference= 2*\pi *3\\\\distance=18.84\\\\time=\frac{distance}{velocity}\\ put\ the\ values\\time=\frac{18.84 feet}{60 \frac{feet}{sec} } \\\\time=0.314\ sec

now, for obtain the  angular velocity , divide  the circumference (use radians  2π radians=360 degrees )by the time it takes to complete a lap

\alpha =\frac{(2 \pi rad)}{time\ per\ lap}\\\\ \alpha =\frac{(2\pi rad)}{0.314 sec}\\ \alpha =20 \frac{rad}{sec}

Have a great day

Phantasy [73]3 years ago
7 0

Answer:

20 rad/sec

Step-by-step explanation:

The formula we are going to use is  v=\omega r

Where

v is the linear velocity (here given 60 ft/s)

\omega  is the angular velocity (what we sought to find)

r is the radius (which is half of diameter, hence, 6/3 = 3 ft)

<em>Plugging these numbers in, we find the angular velocity as:</em>

<em>v=\omega r\\60=\omega*(3)\\\omega=\frac{60}{3}=20</em>

<em />

<u><em>Note: </em></u><em>the units is radians per second (rad/s)</em>

<em />

Correct answer 20 rad/sec

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