Angular Velocity

I think you use the incorrect formula for angular velocity.

Angular velocity is indeed radians per second and it is symbol \(\omega\)

But if you multiply by the radius you get the circumferential velocity, which in this case is the same as the land speed, because the wheel grips the road.

This means \(v = \omega * r\)

\(\omega = v/r\)

\(\omega = {27.78\over{0.5}} = 27.78 * 2=55.56\space \space rad/s\)

Hope this clears it up for you.

A truck with tyres 1 metre in diameter is travelling at 100 km per hour. What is the angular velocity of the tyres in radians per second.

Thanks Guest :)

Mmm, I will just muffle through logically and see if I get the same answer.   

circumference of tyre = \(2\pi r=2\pi*0.5=\pi\;metres\)

100km = 100000m

1hour = 60*60=3600seconds

I use the units to help me work out questions like this.  Units can cancel just like numbers can in fractions...so

I want to find out       \(\frac{radians }{sec}\)

These are the units that I know:

\(\frac{100000m}{hour}\qquad \frac{3600seconds}{hour} \qquad\frac{2\pi\;radians}{revolution}\qquad \frac{\pi \;metres}{revolution}\)

I want radians on the top and seconds on the bottom and I want all the other units to cancel out 

\(\frac{2\pi\;radians}{revolution}\times \frac{1\;revolution}{\pi\;metre}\times \frac{10,000m}{hour}\times \frac{1\;hour}{3600\;seconds}\\ =\frac{2\pi\times 100000\;radians}{3600\pi\;seconds}\\ =\frac{1000\;radian}{18\;seconds}\\ =55.\dot5\;radians/second\)