Question

For what minimum angular speed ${\omega }_{min}$ , will the mass m not slip on the wall?

• A. $\omega =\sqrt{\frac{g}{\mu R}}$
• B. $\omega =2\sqrt{\frac{g}{\mu R}}$
• C. $\omega =\sqrt{\frac{g}{2\mu R}}$
• D. $\omega =\sqrt{\frac{2g}{\mu R}}$

Answer 1

The correct option is A $\omega =\sqrt{\frac{g}{\mu R}}$

For the body not to slip, the frictional force upward should balance the gravitational force downwards, $F_f=mg$ .
$\Rightarrow \mu N=mg\Rightarrow \mu \left(m{\omega }^{2}R\right)=mg$
$\Rightarrow \omega =\sqrt{\frac{g}{\mu R}}$
If the wall is slippery (i.e., no frictional force at all), then no amount of angular speed will be able to keep the object on the wall as the gravitational force downwards is not balanced by any upward force.