Question

complete the sentence below
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 θ is the central angle (in radians) swept out in time t, the linear speed of the object is v = ____ and the angular speed of the object is ω = ____

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 θ is the central angle (in radians) swept out in time t, the linear speed of the object is v = \boxed{} and the angular speed of the object is ω = \boxed{}

Explanation:

Step1: Recall the formula for linear speed

Linear speed \( v \) is defined as the distance traveled \( s \) divided by the time taken \( t \). So, \( v=\frac{s}{t} \).

Step2: Recall the formula for angular speed

Angular speed \( \omega \) is defined as the central angle \( \theta \) (in radians) swept out divided by the time taken \( t \). So, \( \omega = \frac{\theta}{t} \).

Answer:

The linear speed \( v=\boldsymbol{\frac{s}{t}} \) and the angular speed \( \omega=\boldsymbol{\frac{\theta}{t}} \)