If a rolling object has a translational speed of v and a rotational speed of ω,

If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?

If a rolling object has a translational speed of v and a rotational speed of ω, what is the relationship between them for rolling without slipping?

Correct Answer: v = ωR

Step 1: Understand that 'rolling without slipping' means the object rolls on a surface without sliding.
Step 2: Identify the terms: 'v' is the translational speed (how fast the center of the object moves), and 'ω' is the rotational speed (how fast the object spins around its axis).
Step 3: Recognize that when an object rolls without slipping, the point of contact with the ground is momentarily at rest.
Step 4: Relate the translational speed 'v' to the rotational speed 'ω' using the radius 'R' of the object.
Step 5: The formula that connects these speeds is v = ωR, meaning the translational speed equals the rotational speed multiplied by the radius.

Rolling Motion – The relationship between translational speed and rotational speed for an object rolling without slipping.
Kinematics – Understanding the connection between linear and angular motion.