How centripetal is provided while taking turn on level circular track ?

A $70 \;kg$ man stands in contact against the inner wall of a hollow cylindrical drum of radius $3\; m$ rotating about its vertical axis with $200\; rev/min$. The coefficient of friction between the wall and his clothing is $0.15 .$ What is the minimum rotational speed (in $rad/s$) of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

A person with his hands in his pockets is skating on ice at the velocity of $10 \,m/s$ and describes a circle of radius $50\, m$. What is his inclination with vertical

A car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$ . The maximum speed with which the car can move without skidding out is

A curved in a level road has a radius $75\, m$. The maximum speed of a car turning this curved road can be $30 \,m / s$ without skidding. If radius of curved road is changed to $48\, m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........$m / s$.

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m.$ The speed of the car at the top of the hill is between