# Angular velocity of wheel

## Homework Statement

Car runs at 55 mi/hr. and the nail is lodged in tire 13 in from center of wheel, then what is the angular velocity of the nail in rad/hour?

w= v/r

## The Attempt at a Solution

First I will convert 55 miles into inches.
55 mile * 5280 FT/mile * 12 Inches/FT = 3484800 inches.

Velocity = 3484800 INCH/HR
R = 6.5 INCH

Thus:3484800 / 6.5 = 6969600 inch/hr
(Is this correct so far)....
then how do I convert that into rad/hr....?
Is there a formula that I am not aware of?

The formula for angular velocity is v=r(θ/t) where r is the radius, t is time, and theta is the angle in radians, though you can use degrees if I'm not mistaken

But I am not given theta. Not that I am aware of anyways.... I am only given 55 mi/hr and the radius.

actually you are given theta, it is the angle of the wheel, or 2pi radians

O yeah.. so do i multiply 2(pi) times 55 mi/hr / R (in miles)?

not quite. You know that the angle is 2pi radians you need to figure out how long it take to sweep across that distance, in other words how long does it take for the wheel to make one rotation which you can find out since you know how fast the car itself is travelling. θ/t gives you your angular speed. you then multiply by the radius to find the angular velocity.