A circular disc of radius R rolls without slipping along the...

A circular disc of radius $R$ rolls without slipping along the horizontal surface with constant velocity $v_{0}$. We consider a point $A$ on the surface of the disc. Then the acceleration of the point $A$ is: (a) constant (b) constant in magnitude (c) constant in direction (d) constant in magnitude as well as direction

A circular disc of radius $R$ rolls without slipping along the horizontal surface with constant velocity $v_{0}$. We consider a point $A$ on the surface of the disc. Then the acceleration of the point $A$ is:
(a) constant
(b) constant in magnitude
(c) constant in direction
(d) constant in magnitude as well as direction

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

Relative Motion in Rotating Bodies

In a rolling object, every point experiences a combination of the translational motion of the whole body and its rotational motion around the center. Consequently, the acceleration of a point on the surface is a result of both these motions, and its magnitude and direction can change even when the overall velocity of the object is constant.

Centripetal Acceleration

In rotational motion, any point on the object moving in a circular path experiences centripetal acceleration that is always directed toward the center of rotation. This acceleration, which has a magnitude proportional to ?²R for a point at a distance R from the center, continuously changes direction as the point rotates, reinforcing that the acceleration for points on a rolling disc is not constant in direction or magnitude.

Rolling Without Slipping

This concept describes the condition where the rolling object’s point of contact with the surface has zero instantaneous velocity relative to the surface, leading to the relationship v = R?. This is fundamental for linking the translational motion of the object’s center of mass with its rotational motion.

Transcript

Please give Ace some feedback