In the given figure, the sphere rolls without slipping on...

In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity $v_{0}$ - The radius and angular velocity of the sphere is $r$ and $\omega$ respectively. The velocity of centre of mass of the sphere is: (a) $v_{0}+r \omega$ (b) $v_{0}-r \omega$ (c) $r \omega$ (d) $v_{0}$

In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity $v_{0}$ - The radius and angular velocity of the sphere is $r$ and $\omega$ respectively. The velocity of centre of mass of the sphere is:
(a) $v_{0}+r \omega$
(b) $v_{0}-r \omega$
(c) $r \omega$
(d) $v_{0}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rolling Without Slipping

Rolling without slipping is a kinematic condition where the point of contact between a rolling object and the surface has zero relative velocity with respect to that surface. This condition creates a specific relationship between the object's translational speed and its angular speed, typically expressed as v = r * ?, ensuring that there is no skidding at the point of contact.

Relative Motion and Reference Frames

Relative motion involves analyzing the movement of an object by considering the velocities from different reference frames. When an object rolls on a moving platform, the observed velocity in a fixed (ground) frame is determined by adding the object's velocity relative to the platform with the platform's own velocity.

Rotation-Translation Relationship

The rotation-translation relationship in a rolling motion directly connects the linear velocity of the center of mass to the angular velocity through the radius of the object. This relationship is fundamental in scenarios where rolling occurs without slipping, as it ensures that the distance covered by rolling rotation exactly matches the object's linear displacement.

Transcript

Please give Ace some feedback