Physics Homework Help?

Question

A yo-yo is made of two solid cylindrical disks, each of mass 0.047 kg and diameter 0.075 m , joined by a (concentric) thin solid cylindrical hub of mass 0.0052 kg and diameter 0.010 m .

Part A

Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 0.90 m long string, if it is released from rest.

Part B

What fraction of its kinetic energy is rotational?

 

Answer 1

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.

Answer 2

(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 0.5.