If a rolling object has a radius R and rolls with an angular velocity ω, what is

If a rolling object has a radius R and rolls with an angular velocity ω, what is its linear velocity?

If a rolling object has a radius R and rolls with an angular velocity ω, what is its linear velocity?

Step 1: Understand that a rolling object moves in a circular motion.
Step 2: Identify the radius (R) of the rolling object, which is the distance from the center to the edge.
Step 3: Recognize that angular velocity (ω) measures how fast the object is rotating, usually in radians per second.
Step 4: Realize that linear velocity (v) is the speed at which a point on the edge of the object moves in a straight line.
Step 5: Use the formula v = Rω to find the linear velocity, where you multiply the radius (R) by the angular velocity (ω).

Relationship between Angular and Linear Velocity – The linear velocity of a rolling object is directly proportional to its angular velocity and radius, expressed by the formula v = Rω.