A uniform sphere of mass m and radius r rolls without slipping down a inclined plane, inclined at an angle `45^(@)` to the horizontal . Find the magnitude of frictional coefficient at which slipping is absent :

A uniform sphere of mass m and radius R rolls without slipping down an inclined plane set at an angle theta to the horizontal. Find ( a ) the friction coefficient at which slipping is absent, ( b ) the kinetic energy of the sphere t seconds after the beginning of motion.

A uniform sphere of mass m and radius R rolls without slipping down an inclined plane set at an angle theta to the horizontal. Find ( a ) the friction coefficient at which slipping is absent, ( b ) the kinetic energy of the sphere t seconds after the beginning of motion.

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane making an angle 6 with the horizontal. Then its acceleration is.

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane making an angle 6 with the horizontal. Then its acceleration is.

A uniform sphere of mass m and radius R starts rolling without slipping down an inclined plane at an angle alpha to the horizontal. Find the time dependence of the angular momentum of the sphere relative to the point of contact at the initial moment. How will the obtained result change in the case of a perfectly smooth inclined plane?