Question

give an example of pure rolling ,which is combination of two linear motion,with an example???explain answer with daigrammm

i posted it twice,dont give answer untill u r not sure..

Answer 1

the best example of pure rolling can be given with the help of a rigid cylinder rolling down an inclined surface which has a high enough critical coefficiant friction to prevent the cylinder from slipping. before we try to look at a diagram, lets try to understand what rolling actually is.

suppose a cylinder of radius R is rolling on a horizontal surface with velocity v_cm of the center of mass of the cylinder. in rolling, the point in the cylinder in contact with the surface always has a zero relative velocity with the surface.(this is that main condition of rolling without slipping). if the mentioned condition is satisfied the velcity of center of mass can be written as

where is the angular velocity of the cylinder

from the diagram we can see that every point on the cylinder moves with a different velocity. the center of mass moves with a linear velocity, but all other points on the cylinder have different velocities depending in the distance from the C.M and the time. the point on the top A has a velocity . as , the velocity at the point A becomes . simplarly we can show the vecocity of point at B at a particular instant is 0, because Vcm and are directed at opposite directions here.

the above diagram is an example of rolling of a cylider with translational and rotational motions down the slope. as there are two kinds of motion , the cylinder posesses rotational and translational energies as given in the expression the diagram. at the point in the cylinder in contact with the surface, the net force is given by

is the acceleration of the center of mass, is the horizontal accelration due to gravity experienced by the cylinder and f is the frictional force. this net unbalanced force provides a torque to the cylinder which leads to the rolling motion