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

`20 (rad )/(sec)`

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 (feet)/(sec) \\distance= circumference= 2*\pi *r\\diameter=6 feet\\radius=(Diameter)/(2)\ so,r=(6)/(2) =3 feet\\Hence\\\\distance= circumference= 2*\pi *3\\\\distance=18.84\\\\time=(distance)/(velocity)\\ put\ the\ values\\time=(18.84 feet)/(60 (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 =((2 \pi rad))/(time\ per\ lap)\\\\ \alpha =((2\pi rad))/(0.314 sec)\\ \alpha =20 (rad)/(sec)`

Have a great day

Answer 2

20 rad/sec

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=(60)/(3)=20`

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

Correct answer 20 rad/sec