Question

a father fashions a swing for his kids out of a long rope that he fastens to the limb of a tall tree. as one of the kids swings from this rope that is 5.90 m long his tangential speed at the bottom of the swing is 8.80 m/s. what is his angular speed in rad/s?

Explanation:

Step1: Recall the relationship between tangential speed and angular speed

The formula relating tangential speed \(v\), angular speed \(\omega\), and radius \(r\) is \(v = r\omega\). We need to solve for \(\omega\), so \(\omega=\frac{v}{r}\).

Step2: Substitute the given values

Given \(v = 8.80\space m/s\) and \(r = 5.90\space m\). Then \(\omega=\frac{8.80}{5.90}\).

Step3: Calculate the value

\(\omega=\frac{8.80}{5.90}\approx1.49\space rad/s\)

Answer:

\(1.49\space rad/s\)