For linear, or translational, motion an object's resistance to a change in its state of motion is called its inertia and is measured in terms of its mass, in kg.  When a rigid body is rotated, its resistance to a change in its state of rotation is called its rotational inertia, or moment of inertia.  This resistance has a two-fold property.   (1)  The amount of mass present in the object and (2) the distribition of that mass about the chosen axis of rotation.  In general, the formula for an object's moment of inertia is I_CM = kmr² where k is a constant whose value varies from 0 to 1.  Different positions of the axis result in different moments of inertia for the same object; the further the mass is distributed from the axis of rotation, the greater the value of its moment of inertia.  Below is a series of diagrams for a thin rod illustrating how the moment of inertia for the same object can change with the placement of the axis of rotation.

axis on the far end of a thin rod:           I = 16/48 mL2	axis one-fourth of the way from the end of a thin rod:           I = 7/48 mL2	axis at the center of a thin rod:           I = 4/48 mL2

Three other objects whose moments of inertia are important are:  solid spheres, solid disks and cylinders, and thin rings.

solid spheres           I = 2/5 mr2	solid disks and cylinders           I = 1/2 mr2	thin rings           I = mr2

Remember that the smaller the coefficient of mr², the easier it is to accelerate the object. That is, spheres accelerate easier than cylinders, which accelerate easier than thin rings or hoops. That is, hoops has more rotational resistance than cylinders; and cylinders have more resistance than solid spheres.

Law of Conservation of Angular Momentum
I₁ w₁ = I₂ w₂

Angular momentum is conserved whenever there is no external force exerting a torque on the object.  The angular velocity, w, must be measured in radians/sec.  [NOTE:  w = 2pf ]

An example of this occurs in skating. A skater spinning with arms out has a greater I, but a smaller angular velocity compared to when she is spinning with her arms folded in (I is small, angular velocity is large).

Kepler’s 2nd Law: The Law of Equal Areas
A line from the planet to the sun sweeps out equal areas of space in equal intervals of time.

Conservation of angular momentum justifies this relationship.  The moment of inertia for a point mass traveling in a circle is  I = mrČ, gravity is an internal force, and the instantaneous tangential velocity of a point mass, v, equals v = rw. This relationship angular and linear velocities can be understood by imagining a rotating platform.  All points on the platform share the same angular velocity (they all complete the same number of revolutions each second), but each one has a unique linear, tangental, velocity based on how far it is located from the axis of rotation .... that is, how large a circumference it must travel through during each revolution.  The subscript P represents behavior at the Perihelion (the closest position on the left) and the subscript A represents behavior at the Aphelion (the most distant position on the right).

I_P w_P = I_A w_A
mR_P² w_P = mR_A² w_A
R_P² * v_P / R_P = R_A² * v_A / R_A
R_P v_P = R_A v_A
R_P / R_A = v_A / v_P

Thus, the satellite’s speed is inversely proportional to its average distance from the sun.