Q. 98 - Precalculus Enhanced with Graphing Utilities

Question

An object is traveling around a circle with a radius of $2$ meters. If in $20$seconds the object travels $5$ meters, what is its angular speed? What is its linear speed? 

Step-by-Step Solution

Answer

The angular speed is $0.125radians/minute$ and the linear speed is $0.25meter/second$

Step 1. Given information

An object travels around a circle with a radius of $2$ meters and in $20$ seconds the object travels $5$ meters, 

Step 2. Used formulae

• The angular speed is the ratio of the angle travelled $\theta$ and the taken time $t$. That is, angular speed $\omega =\frac{\theta }{t}$
• The linear speed is the ratio of the distance travelled $s$ and the time taken $t$ . that is, $v=\frac{s}{t}$ and also, $\omega =\frac{v}{r}$

Step 3. Calculations

Substituting the values in the mentioned formulae, we get,

The linear speed $v=\frac{5}{20}=\frac{1}{4}=0.25meter/second$

and, the angular speed $\omega =\frac{0.25}{2}=0.125 radians/meter$