Rolling Motion

ROLLING AND SLIPPING:

A disc at any time t = t was moving with linear vel. V₀ and angular vel. ${\omega }_0$. If S is the point of contact then consider the vel. of point S.

${\vec{V}}_{O-e}=V_0$i; ${\vec{V}}_{S-O}=-R{\omega }_0$i

${\vec{V}}_{S-e}={\vec{V}}_{S-O}+{\vec{V}}_{O-e}$

= (V₀ – R${\omega }_0$) i

If vel. of point S is in forward direction with respect to contact surface then body is called is in forward rolling.

If vel. of point S is in backward direction with respect to contact surface then it is called as in bock ward slipping.

And if vel. of point S is 0 then the body is called as in rolling.

So, V₀ – R${\omega }_0$ > 0 $\Rightarrow$ V₀ > R${\omega }_0$ $\Rightarrow$ forward slipping

V₀ – R${\omega }_0$ < 0 $\Rightarrow$ V₀ < R${\omega }_0$ $\Rightarrow$ backward slipping

V₀ – R${\omega }_0$ = 0 $\Rightarrow$ Rolling.

Note:

Suppose a round or spherical object to moving on earth and it is rolling. If at any time t = t its linear acceleration is A and angular acceleration is $\alpha$. Then for further rolling

A = R$\alpha$