Question

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 diameter of the wheel is 6 feet. 10 rad/sec 20 rad/sec 180 rad/sec 360 rad/sec

Answer 1

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

Answer 2

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)

Plugging these numbers in, we find the angular velocity as:

$v=\omega r\\60=\omega*(3)\\\omega=\frac{60}{3}=20$

Note: the units is radians per second (rad/s)

Correct answer 20 rad/sec