Question

A solid uniform disk of mass $m$ rolls without slipping down a fixed inclined plane with an acceleration $a$. If the frictional force on the disk due to surface of the plane is given as $\frac{1}{x}ma$. Find $x$.

Answer 1

Since its given that the disk is not slipping , the net acceleration of the point of contact along the plane of the incline is zero .

$\therefore$ $a=R$$\alpha$

$\alpha$ = $\frac{a}{R}$

Writing torque equation about the center of the disk .

The only force that produces torque is friction .

$f\left(R\right)=I\alpha$

$f\left(R\right)=\frac{m{R}^2}{2}\frac{a}{R}$

$f=\frac{ma}{2}$

$\therefore x=2$