What is rolling motion?

Explanation

(i) It is the combination of pure translational and pure rotational motion.
(I) The rolling motion is the most commonly observed motion in daily life. The motion of wheel is an example of rolling motion. (II) Round objects like ring, disc, sphere etc. are most suitable for rolling. Let us study the rolling of a disc on a horizontal surface. Consider a point P on the edge of the disc. (III) While rolling, the point, undergoes translational motion along with its center of mass and rotational motion with respect to its center of mass.
(ii) (I) If the radius of the rolling object is R, in one full rotation, the center of mass is displaced by `2 pi R` (its circumference).
(II) Not only the center of mass, but all the points on the disc are displaced by the same `2 pi R` after one full rotation. The only difference is that the center of mass takes a straight path, but, all the other points.
(III) Undergo a path which has a combination of the translational and rotational motion. Especially the point on the edge undergoes a path of a cycloid.
(IV) As the center of mass takes only a straight line path, its velocity `v_(CM)` is only translational velocity `v_("TRANS") (v_(CM) = v_("TRANS"))`. All the other points have two velocities. One is the translational velocity `v_("TRANS")`, (which is also the velocity of center of mass) and the other is the rotational velocity `v_("ROT") (v_("ROT") = r omega)`.
(v) Here, r is the distance of the point from the center of mass and `omega` is the angular velocity. The rotational velocity `v_("ROT")` is perpendicular to the instantaneous position vector from the center of mass.
(vi) The resultant of these two velocities is v. This resultant velocity v is perpendicular to the position vector from the point of contact of the rolling ojbect with the surface on which it is rolling as shown in Figure.