Conservation of angular momentum when a system changes configuration.

A uniform cylinder, mass M= 12 kg, radius R= .36 m, is initially rotating about a vertical axis through its center at angular velocity wo= 6.6 rad/sec. Now two small (point masses), each of mass m= 2 kg, are dropped onto and stick to the cylinder, each at distance r= .24 m from the axis. SEE ATTACHMENT for diagram.
Find wf, the final angular velocity of the combined three objects after the drop.

Solution:
<br>Note 1.
<br>If no external torque is applied to a system, its total angular momentum remains constant.
<br>Note 2.
<br>Recall that the angular momentum, L, of a rotating object with moment of inertia I, and angular rotation speed w is:
<br>(1) L= I ...

A uniform rod of mass m_1 and length L rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass m_2, are mounted so that they can slide along the rod. They are initially held by catches at positions a distance r on each side from the center of the rod, and

A solid, horizontal cylinder of mass 10.4 kg and radius 1.13 m rotates with an angular speed of 6.81 rad/s about a fixed vertical axis through its center. A 0.251 kg piece of putty is dropped vertically onto the cylinder at a point 0.864 m from the center of rotation, and sticks to the cylinder. Determine the final angular speed

Suppose a 60kg person stands at the edge of a 6.0m diameter circular platform, which is mounted on frictionless bearings and has a moment of inertia of 1800kgm^2. The platform and runner are initially at rest. Calculate the angular velocity of the platform if the runner begins to run 4.2m/s.

Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from L1 to L2.
Show that the work done in pulling the string equals the increase in kinetic energy of the mass.

Two astronauts (Fig.), each having a mass of 70.0 kg, are connected by a 11.0 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.70 m/s.
(a) Treating the astronauts as particles, calculate the magnitude of the angularmomentum.
(b) Calculate the rotational energy of the syst

A student on a piano stool rotates freely with an angular speed of 3.16 rev/s. The student holds a 1.50 kg mass in each outstretched arm, 0.794 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.45 kg*m2, a value that remains constant. As the student pulls his

A space station is shaped like a giant wheel and has a radius of 100 metres and a moment of inertia of 5.00 x 10^8 kg m^2. A crew of 150 is living on the rim. Assume average mass for a crew member as 65 kg. The station's rotation causes the crew to experience an apparent free-fall acceleration of g. 100 of the crew members m

A 62.99 kg woman stands at the rim of a horizontal turntable having a moment of inertia of 495 kg·m^2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) a