Finding angular velocity?

Question

an auto is traveling at 70 ft/sec. if the wheel diameter is 27 in, what is its angular velocity?

Answer 1

circumference = pi * 27 = 84.823 in = 7.069 ft

70 ft each second; there must be 70/7.069 =9.903 revolutions per second

That is 9.903 * (2*pi) radians per second;

hence the angular velocity, omega = 62.22 rad/s

Answer 2

First, you have to know that the angular velocity is in angle per second, this means that the wheel turns at certain angle every second, and the velocity you were given is the distance the car travels every sec.
SO!
You need to know the wheel perimeter, that is PI*Diameter (it's better to work with ft)
27in = 2.25ft and then the perimeter is 7.07ft
so the tire turns 70 / 7.07 times every sec =9.9 RPM
you could report 10RPM

Answer 3

The wheel circunference is 27*pi inch=7.07feet .So at a speed of 70 feet/s it makes 9.9 turns/s
Each turn equal 2pi radian,so the angular velocity is
w= 9.9*2pi=62.22 rad/s

Answer 4

first we convert ft into meter

w = angular velocity
v = 70ft/sec = 21.336m/s
r = d/2 = 13.5 inch = 1.125ft = 0.3429m


w (omega) = v (velocity) / r (radius)
w = 21.336m/s/0.3429m
w = 62.2rad/s there you are