Chapter 13.1, Problem 8WE

To determine

To find: The angular speed and rim speed of the smaller wheel.

Answer to Problem 8WE

The angular speed of the smaller pulley is $250\pi \raisebox{1ex}{$radian$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$ .

Explanation of Solution

Given information:

The given figure (1)

  

Figure (1)

Calculation:

Calculate the function.

  $\begin{array}{c}v=r\omega \\ =\left(15\right)\left(100\right)\left(3.1416\right)\\ =4712.4\end{array}$

The rim speed of smaller pulley is $1500\pi \raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$ or $4700\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$

Use the formula

  $\omega =\frac{v}{r}$

Substitute the value of $v$

  $\begin{array}{c}\omega =\frac{1500\pi }{6}\\ =250\pi \end{array}$

Therefore the angular speed of the smaller pulley is $250\pi \raisebox{1ex}{$radian$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$ .