1. Circular Motion & Gravitation
Chapter 5
Circular Motion & Gravitation

2. 5-1 Kinematics of Uniform Circular Motion
Uniform circular motion: motion in a circle of constant radius at constant speed
Instantaneous velocity is always tangent to circle.

3. Although the magnitude of the velocity may remain constant the direction of the velocity is constantly changing
Recall that acceleration is the change in velocity over the change in time and is a vector
In circular motion, the direction is constantly changing which means an object moving in circular motion is ALWAYS accelerating, even if it’s velocity remains constant

4. 5-1 Kinematics of Uniform Circular Motion
In circular motion acceleration is called centripetal, or radial, acceleration, aR and it points towards the center of the circle.

5. 5-1 Kinematics of Uniform Circular Motion
The magnitude of aR can be found by the formula
(5-1)
aR and v are always perpendicular to each other

6. 5-2 Dynamics of Uniform Circular Motion
For an object to be in uniform circular motion, there must be a net force acting on it; a centripetal force
We know that
We just saw that aR is
so we can say the rotational force is
(5-1)

7. 5-2 Dynamics of Uniform Circular Motion
There is no centrifugal force pointing outward; only the natural tendency of the object to move in a straight line.
If the centripetal force vanishes, the object flies off tangent to the circle.

8. 5-3 Highway Curves, Banked and Unbanked
If the frictional force is insufficient, the car will tend to move more nearly in a straight line, as the skid marks show.

9. 5-6 Newton’s Law of Universal Gravitation
If the force of gravity is being exerted on objects on Earth, what is the origin of that force?
Newton’s realization was that the force must come from the Earth.
He further realized that this force must be what keeps the Moon in its orbit.

10. 5-6 Newton’s Law of Universal Gravitation
By observing planetary orbits Newton proposed his law of Law of Universal Gravitation
Every particle in the universe attracts every other particle
This force acts along the line joining the two particles
Where G is a universal constant

11. 5-9 Kepler’s Laws and Newton's Synthesis
Even before Newton, Johannes Kepler studied and described the motion of the planets ( )
His findings are now summarized in Kepler’s laws of planetary motion

12. Kepler’s first law
The path of each planet around the Sun is an ellipse with the sun at one focus

13. Kepler’s second law
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time

14. Kepler’s third law
The ratio of the squares of the period T of any 2 planets revolving around the Sun is equal to the ratio of the cubes of their mean distances s from the Sun
T is the period and r is the orbit radius

15. 5-10 Types of Forces in Nature
Modern physics currently recognizes four fundamental forces:
Gravity
Electromagnetism (sometimes combined with the weak nuclear force and called the Electroweak force)
Weak nuclear force (responsible for some types of radioactive decay)
Strong nuclear force (binds protons and neutrons together in the nucleus)
Other everyday observations (such as friction) are not fundamental forces, but one of these four

16. 5-10 Types of Forces in Nature
So far we’ve only talked about gravity; the weakest of the 4 forces
Other forces will come up as the year progresses
Physicists have been working on trying to unify these theories into one grand unified theory, or GUT. Also called the theory of everything or TOE.
TOE and GUTs are very popular and controversial in physics!

17. References
Giancoli, Douglas. Physics: Principles with Applications 6th Edition
Zitewitz. Physics: Principles and Problems. 2004