A small sphere of mass m and radius r rolls without slipping on the insides of a large hemisphere of radius R whose axis of symmetry is vertical. Its starts at the top from rest. What is the kinetic energy of the small sphere at the bottom? What fraction is rotational and what transiational? What normal force does the small spheres exert on the hemisphere at the bottom?
[Hint: consider circular motion of center of mass at the bottom to calcualte normal reaction. For others consider conservation of energy.?

A small steel sphere of mass m and radius r rolls without slipping on the fiictionless surface of a large hemisphere of radius R{R gt gt r) whose axis of symmetry is vertical. It starts at the top from the rest, (a) What is the kinetic energy at the bottom ? (b) What fraction is the rotational kinetic energy of the total kinetic energy at the bottom? (b) What fraction is the rotational kinetic energy of the total kinetic energy? (c) What fraction is the translational kinetic energy of the total kinetic energy? (d) Calculate the normal force that the small sphere will exerton.the hemisphere at its bottom. Howthe results will be affected if r is not very sjnall as compared to R.

A small steel sphere of mass m and radius r rolls without slipping on the fiictionless surface of a large hemisphere of radius R {R gt gt r) whose axis of symmetry is vertical. It starts at the top from the rest, (a) What is the kinetic energy at the bottom ? (b) What fraction is the rotational kinetic energy of the total kinetic energy ? (c) What fraction is the rotational kinetic energy of the total kinetic energy? (d) What fraction is the translational kinetic energy of the total kinetic energy?

A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

A small sphere D of mass and radius rols without slipping inside a large fixed hemispherical radius R( gt gt r) as shown in figure. If the sphere starts from rest at the top point of the hemisphere normal force exerted by the small sphere on the hemisphere when its is at the bottom B of the hemisphere. .

A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R.At what height will the ball lose contact with surface of the sphere?

A solid sphere of mass m rolls down an inclined plane without slipping from rest at the top of an inclined plane.The linear speed of the sphere at the bottom of the inclined plane is v .The kinetic energy of the sphere at the bottom is

A small ball of radius r rolls without sliding in a big hemispherical bowl. of radius R. what would be the ratio of the translational and rotaional kinetic energies at the bottom of the bowl.

A small ball of radius r rolls without sliding in a big hemispherical bowl. of radius R. what would be the ratio of the translational and rotaional kinetic energies at the bottom of the bowl.