Chapter 5

Circular Motion & Gravitation

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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.

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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

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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.

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5-1 Kinematics of Uniform Circular MotionThe magnitude of aR can be found by the formula

(5-1)

aR and v are always perpendicular to each other

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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)6

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.

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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.

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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.

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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

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5-9 Kepler’s Laws and Newton's Synthesis

Even before Newton, Johannes Kepler studied and described the motion of the planets (1571-1630)

His findings are now summarized in Kepler’s laws of planetary motion

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Kepler’s first lawThe path of each planet around the Sun is an ellipse with the sun at one focus

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Kepler’s second lawEach planet moves so that an imaginary line

drawn from the Sun to the planet sweeps out equal areas in equal periods of time

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Kepler’s third lawThe 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

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5-10 Types of Forces in NatureModern physics currently recognizes four

fundamental forces:

1. Gravity

2. Electromagnetism (sometimes combined with the weak nuclear force and called the Electroweak force)

3. Weak nuclear force (responsible for some types of radioactive decay)

4. 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 four15

5-10 Types of Forces in NatureSo far we’ve only talked about gravity; the

weakest of the 4 forcesOther forces will come up as the year progressesPhysicists 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!

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ReferencesGiancoli, Douglas. Physics: Principles with

Applications 6th Edition. 2009. Zitewitz. Physics: Principles and Problems.

2004

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