Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

An object travels around a circle of radius $r$ with constant speed. If $s$ is the distance traveled in time $t$ around the circle and $\theta$ is the central angle (in radians) swept out in time $t$ , then the linear speed of the object is $v=\_\_\_\_\_\_\_\_$ and the angular speed of the object is $w=\_\_\_\_\_\_\_\_$ .

Step-by-Step Solution

Answer

The solution is $\frac{s}{t} , \frac{\theta }{t}$ .

Step 1. Given information

An object travels around a circle of radius $r$ with constant speed. The distance traveled is $s$ in time $t$ around the circle and $\theta$ is the central angle (in radians) swept out in time $t$ .

Step 2. Calculation

An object travels around a circle of radius $r$ with constant speed. If $s$ is the distance traveled in time $t$ around the circle and $\theta$ is the central angle (in radians) swept out in time $t$, then the linear speed of the object is $v=\frac{s}{t}$ and the angular speed of the object is $w=\frac{\theta }{t}$ .