Chapter 13.1, Problem 10WE

To determine

To find: The angular speed in radians per second

Answer to Problem 10WE

The velocity of the hour is about $0.0073\raisebox{1ex}{$\mathrm{m}m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Explanation of Solution

Given information:

The given function the hand is $5cm$ long.

Calculation:

Calculate the function.

  $\begin{array}{c}\omega =\frac{\theta }{t}\\ =\frac{2\pi }{43200}\\ =0.00015\raisebox{1ex}{$radian$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.\end{array}$

The angular speed of the hour hand is $0.00015\raisebox{1ex}{$radian$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$

The velocity of the product of radius and angular velocity

  $\begin{array}{c}r\omega =50\left(0.00015\right)\\ =0.0073\raisebox{1ex}{$\min $}\!\left/ \!\raisebox{-1ex}{$s$}\right.\end{array}$

Therefore the velocity of the hour is about $0.0073\raisebox{1ex}{$\mathrm{m}m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$