Physics

Physics

Problem

Which of the following conditions must be satisfied for the relation v=rωv = r\omega to describe a rigid object that is moving across a horizontal surface? a) A non-zero coefficient of kinetic friction is acting between the object and the surface. b) The point of contact between the object and the surface is instantaneously at rest relative to the surface. c) The object’s center of mass moves with constant velocity. d) The net external torque on the object about its center of mass is zero.
Intuitive explanation

The key is recognizing that v=rωv = r\omega links linear and angular velocity, but only when there's a specific constraint on how the object moves. This relation assumes the object is rolling without slipping—meaning the contact point with the ground has zero velocity relative to the surface. Without this no-slip condition, the object could slide, skid, or spin freely, breaking the direct proportionality between vv and ω\omega. Think of it as the ground "locking" the rotation to the translation.

Intuitive explanation

The key is recognizing that v=rωv = r\omega links linear and angular velocity, but only when there's a specific constraint on how the object moves. This relation assumes the object is rolling without slipping—meaning the contact point with the ground has zero velocity relative to the surface. Without this no-slip condition, the object could slide, skid, or spin freely, breaking the direct proportionality between vv and ω\omega. Think of it as the ground "locking" the rotation to the translation.

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