Circular Motion -- Things to know and be able to do on the test:

** I typed this up rather quickly, and, therefore, I do not solemnly swear that this is a truly comprehensive list of everything you need to know.  But it should at least be close.

·         Know and apply Kepler’s three laws

·         Given a diagram of a satellite’s elliptical orbit, be able to…

o   Compare transit time intervals between pairs of points in the orbit

o   Draw velocity and gravitational force vectors for the satellite at various points in its orbit, with lengths proportional to magnitude

o   Compare speeds at different points in the orbit

·         Understand the factors that determine gravitational force and g (acceleration due to gravity)

·         Know the difference between orbital radius and altitude

·         Know that net force acting on an object undergoing uniform circular motion (even if it’s just moving through one small arc of a circle) is always equal to mv²/r

·         Solve problems with uniform circles.  Solve for variables (e.g. radius, mass, velocity, normal force, tension…)

o   horizontal circles on Earth (vertical axes)

§  balls on strings or

§  cars driving in circles

§  Centrifuges

o   circles in space

§  objects orbiting planets

§  artificial gravity in rotating space stations

o   vertical circles on Earth (horizontal axes)

§  Objects on the inside of the circle, with a normal force or tension pushing (or pulling) inward.

§  Objects on the outside of the circle, with a normal force pushing outward (only works if the object is on the top of the circle; otherwise the object falls off)

·         Know that the sensation of a 1 g comes is produced by a normal force equal to one’s weight on Earth’s surface.

·         Know that scale’s readings provide the normal force exerted by the scale’s surface on the object that’s touching the scale.

·         Find the gravitational force between two spheres that are touching.

·         Use Kepler’s 3^rd Law to find the period or orbital radius of a satellite.

·         Use a data table to find the necessary information to solve problems relating to satellites and orbits.  This data may not be given in the problem, although the problem should say something like “use the data table…”

·         Without Kepler’s 3^rd Law, find one of the following:

·         Equations involving objects in circular orbits:

o   Know or derive a formula for g, in terms of G, M, and r.

o   Know or derive a formula for v, in terms of G, M, and r.

o   Know or derive a formula for v in terms of T and r

o   Use the above equations to find: orbital radius, mass of orbited object, satellite velocity, satellite period of rotation, or g

·         Know which equations (all except Kepler’s 3^rd Law) require specific units.  Be able to convert to those units when necessary.

·         Know Earth’s orbital T and distance from the Sun, in AU.