For a banked curved road,if the velocity of the vehicle $v < v_0$ (where $v_0$ is the optimum speed),what is the direction of the frictional force?

$A$ $0.5 \ kg$ mass is in contact against the inner wall of a cylindrical drum of radius $4 \ m$ rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5 \ rad/s$. The coefficient of friction between the drum's inner wall surface and mass is . . . . . . . (Take $g = 10 \ m/s^2$)

$A$ bike moving at a speed of $60 \; km/hr$ takes a turn with a radius of $0.1 \; km$. At what angle with the vertical should the bike be tilted to avoid slipping?

$A$ large drum having radius $R$ is spinning around its axis with angular velocity $\omega$,as shown in the figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum,taking the coefficient of friction between the drum surface and mass $M$ as $\mu$,is:

$A$ child is on a merry-go-round,standing at a distance $2 \ m$ from the centre. The coefficient of static friction between the child and the surface of the merry-go-round is $0.8$. At what maximum angular velocity can the merry-go-round be rotated before the child slips (in $rad/s$)? (Take $g = 10 \ m/s^2$)

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu$ is