Question

1. a rock stuck in a bike tire moves in a horizontal circle with uniform circular motion, 0.33 m away from the center of the wheel. it completes a revolution in 6.4 - 10^{-2} s. what is the rocks linear velocity if it were flung out of the tire? 0.3 m/s 3.2 m/s 5.2 m/s 32.4 m/s clear all

Explanation:

Step1: Calculate the circumference of the circular path

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r=0.33\space m\), then \(C = 2\pi\times0.33\space m\approx 2.073\space m\)

Step2: Use the formula for linear velocity \(v=\frac{d}{t}\)

Here, \(d = C\) (distance traveled in one revolution) and \(t = 6.4\times10^{-2}\space s\). So \(v=\frac{2.073}{6.4\times 10^{-2}}\space m/s\)

$$v=\frac{2.073}{0.064}\space m/s\approx 32.4\space m/s$$

Answer:

\(32.4\space m/s\) (the fourth option)