Question

1. (5pts) a tractor has front wheels that are smaller than the back wheels. if the back wheels have a radius of 2 m and turn at ω = 40 rad/s, what is the linear speed of the tractor? if the front wheel has half the radius of the rear wheel, at what angular speed does it turn for the linear speed you just found?

Explanation:

Step1: Calculate the linear speed of the back - wheel

The formula for linear speed \(v = r\omega\). Given \(r = 2m\) and \(\omega=40rad/s\)
\(v = 2\times40\)
\(v = 80m/s\)

Step2: Calculate the angular speed of the front - wheel

The linear speed of the front - wheel is the same as that of the back - wheel (\(v = 80m/s\)). The radius of the front - wheel \(r_{front}=\frac{2}{2}=1m\)
Using the formula \(\omega=\frac{v}{r}\), substituting \(v = 80m/s\) and \(r = 1m\)
\(\omega=\frac{80}{1}\)
\(\omega = 80rad/s\)

Answer:

The linear speed of the tractor is \(80m/s\) and the angular speed of the front - wheel is \(80rad/s\)