Answer:
Minimum speed will be 2.7576 rad/sec
Explanation:
We have given radius of the room r = 2.15 m
Coefficient of friction between the child and wall [tex]\mu =0.6[/tex]
Centripetal force acting on the child is given by [tex]F_C=\frac{mv^2}{r}[/tex], here m is mass r is radius and v is velocity
The normal force will balance the centripetal force
So [tex]N=\mu F_C[/tex]
[tex]\mu \frac{mv^2}{r}=mg[/tex]
[tex]v=\sqrt{\frac{rg}{\mu }}=\sqrt{\frac{2.15\times 9.81}{0.6}}=5.9289m/sec[/tex]
We know that [tex]v=r\omega[/tex]
So [tex]\omega =\frac{v}{r}=\frac{5.9289}{2.15}=2.7576rad/sec[/tex]
