Question

1. What is the direction of the angular momentum for the rotation of the Earth?

2. If you give a hard boiled egg a spin on the table, it will keep spinning for a long time. If you do the same with an uncooked egg, it stops relatively quickly. Explain this.

3. A dumbbell consists of two uniform spheres of mass M and radius R, joined by a thin rod of radius r and length l and mass m.

a) What is the moment of inertia about an axis perpendicular to the rod, through the center of mass?

b) What is the moment of inertia about an axis parallel to the rod, through the center of mass?

4. A meterstick is initially standing vertically on a frictionless floor. A small gust of wind makes it begin to fall. At what angular velocity will it hit the floor?

Answer 1

1)

The line joining South pole to the North pole is the axis of rotation of Earth. 'The direction of angular momentum of Earth is along South pole to North pole.

2)

The raw egg will stop quickly compared to the boiled egg, because the inner liquid layers of raw egg will rub against each other. Hence the energy is lost through friction and viscosity. This does not happen in the boiled egg.

3)

a) about an axis perpendicular to the rod, through the center of mass

moment of inertia is

b)

about an axis parallel to the rod, through the center of mass

moment of inertia is

4)

The meterstick slides such that the center of mass moves along a vertical straight line through the initial position of center of mass. Let the velocity ofcenter of mass and the angular velocity at any instant be and .

Let be the angle between vertical and rod at the same incident. since the lower end of the rod is sliding along the horzontal surface

Total kinetic energy of the rod at this instant is is the loss in potential energy

Finally when the rod will be almost horzontal and