great concepts about rolling motion
Rolling Motion or Combined rotation and translation
A body which is not only rotating but also translating is said to make rolling motion.
- The displacements of all points in the body are different (generally except when it has made complete revoultions).
- The centre of mass always has a translational motion (no rotational motion).
- This is valid if the axis of rotation is the centre of mass as otherwise there will be a pseudo torque that we would have to consider.
Rolling motion can be of three types:
- Pure rolling or rolling without slipping: In this case distance travelled by the centre of mass is equal to 2R.
- Rolling with forward slipping: in this case the distance travelled by the centre of mass is more than 2R.
- Rolling with backward slipping: in this case the distance travelled by the centre of mass is less than 2R.
- Displacement, velocity and acceleration of any point P on the body can be calculated by:
s = scm + sp,cm where all terms are vector quantities
v=vcm + vp,cm
a = acm + ap,cm
- V=R is not the defining equation of pure rolling. This is only valid if the surface on which the body is rolling is stationary.
- If the surface is not stationary, then defining equation is acceleration of point of contact with respect to the moving surface is zero.
- Friction is necessary for rollling motion. This is not true. When a body is already in pure rolling there is no frictional force acting on the body. Similarly, if a force is applied tangentially on the top of a ring then no friction is necessary to continue pure rolling.
- In rolling motion, friction acts in a direction so as to ensure that acceleration of point of contact is zero regardless of whether it promotes or slows down motion.
- Work done by friction in pure rolling is zero as the point of contact remains at rest relative to the surface hence the displacement of the point of contact is zero.