Answer:
20 rad/sec
Step-by-step explanation:
The formula we are going to use is [tex]v=\omega r[/tex]
Where
v is the linear velocity (here given 60 ft/s)
[tex]\omega[/tex] 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:
[tex]v=\omega r\\60=\omega*(3)\\\omega=\frac{60}{3}=20[/tex]
Note: the units is radians per second (rad/s)
Correct answer 20 rad/sec
Answer:
[tex]20 \frac{rad }{sec}[/tex]
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
[tex]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[/tex]
now, for obtain the angular velocity , divide the circumference (use radians 2π radians=360 degrees )by the time it takes to complete a lap
[tex]\alpha =\frac{(2 \pi rad)}{time\ per\ lap}\\\\ \alpha =\frac{(2\pi rad)}{0.314 sec}\\ \alpha =20 \frac{rad}{sec}[/tex]
Have a great day
