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?

Short answer

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

Step-by-step solution

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$\omega =\frac{0.25}{2}=0.125radians/meter$