A particle of mass m moves along the internal smooth surface of a vertical cylinder of the radius R. Find the force with which the particle acts on the cylinder wall if at the initial moment of time its velocity equals `v_(0)`. And forms an angle `alpha` with the horizontal.

A heavy particle of mass m is in motion on a smooth surface of hemisphere of radius R and there is no friction. At the initial instant the particle is at the topmost point A and has an initial velocity v_(0) At what point will the particle leave the surface of the hemisphere ? Also determine the value of v_(0) for which the particle will leave the sphere at the initial instant.

Find the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Find the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Find the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder.

A particle of mass m moving with a speed v hits elastically another stationary particle of mass 2m on a smooth horizontal circular tube of radius r. The time in which the next collision will take place is equal to