# Angular Velocity of a Rolling Sphere

on . Posted in Classical Mechanics

Angular velocity of a rolling sphere, abbreviated as $$\omega$$ (Greek symbol omega), is the rate at which the sphere rotates around its own axis as it moves forward.  The angular velocity is directly proportional to the linear velocity and inversely proportional to the radius of the sphere.  When a sphere is rolling without slipping (not skidding or sliding on its surface), the relationship between its linear velocity, angular velocity, and radius holds true.  This concept is commonly used in physics to describe the motion of rolling objects.

## Angular Velocity of a Rolling Sphere formula

$$\large{ \omega = \frac{ v }{ r } }$$
Symbol English Metric
$$\large{ \omega }$$   (Greek symbol omega) = angular velocity $$\large{\frac{deg}{sec}}$$  $$\large{\frac{rad}{s}}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ r }$$ = radius of a sphere $$\large{ ft }$$ $$\large{ m }$$ 