$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

$A$ $0.5 \ kg$ 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 $g = 10 \ m/s^2$)

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

Find the maximum velocity for skidding for a car moved on a circular track of radius $100 \, m$. The coefficient of friction between the road and tyre is $0.2$.

How is centripetal force provided during motion on a level circular path?

$A$ motorcyclist rides in a horizontal circle about a central vertical axis inside a cylindrical chamber of radius $r$. If the coefficient of friction between the tyres and the inner surface of the chamber is $\mu$,what is the minimum speed of the motorcyclist to prevent him from skidding? ($g$ = acceleration due to gravity)