Homework #3 is due tomorrow Tuesday, Sept. 29, 5:00 pm Exam #1 on Wednesday It will cover the material covered in the nine class sessions to date Review session: Tuesday, Sept. 29, 7:15-8:15 pm, SW218

Matter, Forces and Motion

Scalars and Vectors Scalar: a quantity described solely by its size (and units) Vector: a quantity described by its size AND direction

speed – rate at which an object moves [e.g., m/s]. A scalar quantity. velocity – an object’s speed AND direction, [e.g.,10 m/s east]. A vector quantity. acceleration – a change in an object’s velocity, i.e., a change in speed OR direction [m/s2]. A vector quantity.

Force, momentum, and acceleration are all vectors Momentum (p) – the mass of an object times its velocity (p=mv) Force (f) – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, a force causes a change in velocity, or an acceleration (a) Force, momentum, and acceleration are all vectors

Forces and Newton’s Laws of Motion

Newton’s First Law of Motion A body in motion remains in motion and a body at rest remains at rest unless acted upon by an outside force. OR If the net force acting on an object is zero, then there is no change in the object’s motion.

What happens when there are forces?

F = rate of change of momentum Newton’s Second Law of Motion The change in a body’s velocity due to an applied force is in the same direction as the force, and is proportional to the force, but is inversely proportional to the body’s mass. F = ma Or F = rate of change of momentum

Because force is a vector, forces only affect motion in the direction of the force. Motion perpendicular to the force is unchanged.

F = ma can be rewritten to show that for a given force, the acceleration is inversely proportional to the mass: a = F / m

Do not confuse mass and density Mass = amount of matter Density = amount of matter per volume Higher density means more matter packed into same volume

Both p and v are vector quantities Momentum: p = mv Both p and v are vector quantities

Law of Conservation of Momentum If the net force acting on an object is zero, then the total momentum of a system remains constant.

Newton’s Third Law of Motion “For every applied force, a force of equal size but opposite direction arises” or For every action there is an equal and opposite reaction

F = ma (= rate of change of momentum) Newton's Laws of Motion A body in motion remains in motion and a body a rest remains at rest unless acted upon by an outside force. F = ma (= rate of change of momentum) For every applied force, a force of equal size but opposite direction arises.

Major Conservation Laws Conservation of energy Conservation of momentum Conservation of angular momentum

Angular Momentum angular momentum – the momentum involved in spinning /circling = mass x velocity x radius torque – anything that can cause a change in an object’s angular momentum (twisting force)

Conservation of Angular Momentum In the absence of a net torque, the total angular momentum of a system remains constant.

Forces change momentum Torques change angular momentum

Gravity & Orbits Gravity provides this force. A planet is always changing its direction of motion. Newton’s second law therefore states that a force must be acting on the planet. Gravity provides this force.

Angular Momentum & Orbits The angular momentum of an orbiting planet is conserved, i.e., it is always the same. This provides yet another reason why planets move fastest at perihelion and slowest at aphelion.

Which situation(s) does NOT describe an acceleration: a) a car traveling with constant speed on a straight road. b) a car traveling with constant speed around a bend. c) a planet traveling in its orbit around the Sun. d) a car decreasing speed on a straight road. e) an electron traveling around a nucleus.

Which situation(s) does NOT describe an acceleration: a) a car traveling with constant speed on a straight road. b) a car traveling with constant speed around a bend. c) a planet traveling in its orbit around the Sun. d) a car decreasing speed on a straight road. e) an electron traveling around a nucleus.

a) throw the hammer at the space ship to get someone's attention. You are an astronaut taking a spacewalk to fix your spacecraft with a hammer. Your lifeline breaks and the jets on your back pack are out of fuel. To return safely to your spacecraft (without the help of someone else), you should a) throw the hammer at the space ship to get someone's attention. b) throw the hammer away from the space ship. c) use a swimming motion with your arms. d) kiss your ship good bye.

a) throw the hammer at the space ship to get someone's attention. You are an astronaut taking a spacewalk to fix your spacecraft with a hammer. Your lifeline breaks and the jets on your back pack are out of fuel. To return safely to your spacecraft (without the help of someone else), you should a) throw the hammer at the space ship to get someone's attention. b) throw the hammer away from the space ship. c) use a swimming motion with your arms. d) kiss your ship good bye.

A gram of lead has a greater ______ than a gram of feathers. a) mass. b) density. c) weight. d) volume.

A gram of lead has a greater ______ than a gram of feathers. a) mass. b) density. c) weight. d) volume.

Since angular momentum is conserved, the rotational speed of a collapsing gas cloud a) depends on its mass. b) increases. c) decreases. d) is independent of its initial rotation.

Since angular momentum is conserved, the rotational speed of a collapsing gas cloud a) depends on its mass. b) increases. c) decreases. d) is independent of its initial rotation.

Since angular momentum is conserved, the orbital speed of a planet at perihelion as compared to aphelion a) is larger. b) is smaller. c) is the same. d) approaches infinity.

Since angular momentum is conserved, the orbital speed of a planet at perihelion as compared to aphelion a) is larger. b) is smaller. c) is the same. d) approaches infinity.

The Acceleration of Gravity (a force) As objects fall, they accelerate (a = g = Fgrav/m). We use the special symbol g to represent the acceleration due to the force of gravity. At sea level on the Earth, g = 9.8 m/s each second, or g = 9.8 m/s2. The higher you drop the ball, the greater its velocity will be at impact (force will be acting on it longer).

Weight is the force of gravity acting upon an object : W = Fg = mg

Galileo demonstrated that g is the same for all objects, regardless of their mass!

Is Mass the Same Thing as Weight? mass – the amount of matter in an object weight – a measurement of the force due to gravity acting upon an object W = mg (weight) F = ma When in free-fall, you still have weight! “weightless” is a misnomer

Objects do have weight in space Free-fall often confused with weightlessness

Concept Test You are more strongly attracted (by gravity, that is) towards your larger friends than towards your smaller friends. true false

Concept Test You are more strongly attracted (by gravity, that is) towards your larger friends than towards your smaller friends. true

Concept Test If you go to the moon, where the acceleration of gravity is weaker, your mass changes, but your weight stays the same your weight changes, but your mass stays the same your mass and weight both change your mass and weight both stay the same

Concept Test If you go to the moon, where the acceleration of gravity is weaker, your mass changes, but your weight stays the same your weight changes, but your mass stays the same your mass and weight both change your mass and weight both stay the same

Concept Test If you buy a pound of chocolate on the moon, you get more chocolate than you would on the Earth. True False

Concept Test If you buy a pound of chocolate on the moon, you get more chocolate than you would on the Earth. True

Concept Test If you weigh yourself in your friend’s apartment on the 2nd floor of your apartment building, you will weigh more than you do in your 31st floor apartment true false

Concept Test If you weigh yourself in your friend’s apartment on the 2nd floor of your apartment building, you will weigh more than you do in your 31st floor apartment true

Tidal Forces Because the gravitational force decreases with (distance)2, the attractive force experienced by one object (e.g., the Earth) due to the gravitational field of a second object (e.g., the Moon) varies with position (closest parts attracted most strongly).  

  Now look at what happens when we measure the forces relative to the center of the Earth. 

Tidal Friction

Tidal Friction This fight between Moon’s pull & Earth’s rotation causes friction. Earth’s rotation slows down (1 sec every 50,000 yrs.) Conservation of angular momentum causes the Moon to move farther away from Earth.

Synchronous Rotation …is when the rotation period of a moon, planet, or star equals its orbital period about another object. Tidal friction on the Moon (caused by Earth) has slowed its rotation down to a period of one month. The Moon now rotates synchronously. We always see the same side of the Moon. Tidal friction on the Moon has ceased since its tidal bulges are always aligned with Earth.

Most of the large moons in the solar system are in synchronous rotation.