A yo -yo is made up of two cyllindrical disks.

Mass of the each cyllindrical disk is kg.

Diameter of the each disk is m.

Radius of the each disk is  m.

Length of the string is m.  

Cyllindrical disks are joined by the  thin solid cylindrical hub of mass kg.

Total mass of yo-yo is .

Law of conservation of energy:

Gravitational potential energy = Rotational kinetic energy + Linear kinetic energy.
\

Since , .

For a solid cylindrical disk, moment of inertia is .

Substitute corresponding values in the the expression.

.

Linear speed of yo-yo is 3.42 m/s.

(b)  \ \

Find the fraction of the kinetic energy that is rotational.

Substitute corresponding values in the the expression.

.

Fraction of the rotational kinetic energy is 0.493.