Slipping, Spinning and Rolling

(1) Slipping: When the body slides on a surface without rotation then its motion is called slipping motion.

In this condition friction between the body and surface F = 0.

 

Body possess only translatory kinetic energy K_r = ½ mv².

Example : Motion of a ball on a frictionless surface.

(2) Spinning : When the body rotates in such a manner that its axis of rotation does not move then its motion is called spinning motion.                                      

In this condition axis of rotation of a body is fixed.

Example : Motion of blades of a fan.

In spinning, body possess only rotatory kinetic energy K_R = ½ Iω².

Or              K_R = ½ mK² (v²/R²) = ½ mv² (K²/R²).

i.e., Rotatory kinetic energy =(K²/R²) times translatory kinetic energy.

Here (K²/R²) is a constant for different bodies. Value of (K²/R²)  = 1 (ring), (K²/R²) = ½ (disc) and  (solid sphere)

(3) Rolling : If in case of rotational motion of a body about a fixed axis, the axis of rotation also moves, the motion is called combined translatory and rotatory.            

Example : (i) Motion of a wheel of cycle on a road.

                    (ii) Motion of football rolling on a surface.

In this condition friction between the body and surface F ≠ 0.

Body possesses both translational and rotational kinetic energy.

Net kinetic energy = (Translatory + Rotatory) kinetic energy.

K_N = K_T + K_R = ½ mv² + ½ Iω² = ½ mv² + ½ mv² (K²/R²)

\           K_N = ½ mv² (1 + (K²/R²))