Question

A person is riding a bicycle, and its wheels have an angular velocity of 13.1 rad/s. Then, the brakes are applied and the bike is brought toa uniform stop. During braking, the angular displacement of each wheel is 10.9 revolutions. (a) How much time does it take for the biketo come to rest? (b) What is the anguar acceleratioh (in rad/s²) of each wheel?

Answer 1

First, let's convert the displacement to radians:

$10.9\text{ rev}=10.9\cdot2\pi\text{ rad}=21.8\pi\text{ rad}$

Now, let's calculate the angular acceleration using Torricelli's equation:

$\begin{gathered} V^2=V_o^2+2\cdot a\cdot d\\ \\ 0=13.1^2+2\cdot a\cdot21.8\pi\\ \\ 43.6\pi a=-171.61\\ \\ a=\frac{-171.61}{43.6\pi}\\ \\ a=-1.253\text{ rad/s^^b2} \end{gathered}$

Now, to calculate the time, we can use the formula below:

$\begin{gathered} V=V_o+at\\ \\ 0=13.1-1.253t\\ \\ 1.253t=13.1\\ \\ t=\frac{13.1}{1.253}\\ \\ t=10.45\text{ s} \end{gathered}$