Example 1

A 2 kg particle moves at a constant speed of 3.5 m/s around a circle of radius 4 m.

a). What is its angular momentum about the center of the circle?

b). What is its moment of inertia about an axis through the center of the circle and perpendicular to the plane of the motion?

c). What is the angular speed of the particle?

Which position will have a higher rotational speed?

A B

1). Position A

2). Position B

3). Both A and B will have the same rotational speed.

Example 2

You stand on a frictionless platform that is rotating with an angular speed of 1.5 rev/s. Your arms are outstretched, and you hold a heavy weight in each hand. The moment of inertia of you, the extended weights, and the platform is 6 kgm². When you pull the weights in toward your body, the moment inertia decreases to 1.8 kg m².

a). What is the resulting angular speed of the platform?

b). What is the change in kinetic energy of the system?

c). Where did this increase in energy come from?

Torque – Angular Momentum Relationship

Example 3

A disk of mass 2 kg and radius 10 cm is rotating about a frictionless shaft with an initial angular speed of 5 rev/s. It drops onto a second disk of mass 4 kg and radius 10 cm, which is initially at rest. Because of the surface friction, the two disks eventually attain a common angular speed. Find the final angular speed of the system.

Example 4

A 1 kg ball moves with 2 m/s speed in a circle of radius 1 m on a frictionless table. The ball is attached to a string that passes through a hole in the table. The string is pulled downward so that the ball moves in a smaller circle of radius.

a). Find the velocity of the ball when the radius is 0.5 m.

b). Find the tension of the string when the radius is 0.5 m.

Example 5

A thin rod of mass 2 kg and length 1 m is attached to a pivot at the top. A particle of mass 0.5 kg and speed 3 m/s hits the rod at a distance 0.6 m from the pivot and stick to it. Find the kinetic energies before and after the collisions.