Understanding Motion, Energy, and Gravity

Speed:

Rate at which object moves

speed =

distance / time [units of m/s]

Velocity:

Speed and direction

Acceleration:

Rate of change in velocity units of speed/time (m/s²)

All falling objects accelerate at

the same rate (not counting
friction of air resistance)

On Earth, g ≈

m/s² ; speed increases 10 m/s with each
second of falling

t =

time

v =

velocity

Galileo showed that g is the

same for all falling objects, regardless of their mass

Momentum =

mass × velocity

A net force changes

momentum, which generally means an acceleration (change in velocity)

Rotational momentum of a spinning or orbiting object is
known as

angular momentum

Angular momentum describes

objects that are spinning or moving in circles

a torque is

A special force needed to change an object's angular momentum

Mass

a measure of the amount of matter in an object

Weight

the force that a scale exerts upon an object

Objects are weightless

when in free-fall

The gravitational force on the Moon is weaker than on the
Earth. This means that on the Moon:

weight is less, mass is the same

in space,

there is gravity

Weightlessness is due to

a continued state of free-fall

to orbit Earth, a projectile must travel

8000 m in the time it takes to fall 5 m

The Earth's curvature drops a vertical distance of

5 meters for each 8000 m tangent to the surface

speed =

distance / time

Speed and direction →

velocity

Change in velocity →

acceleration

Momentum =

mass × velocity

Force causes

change in momentum, producing acceleration

Mass is

quantity of matter

Weight is

force acting on mass

Sir Isaac Newton

Built on the idea of one universe, discovered laws of motion and
gravity, and much more

Newton's first law of motion:

An object moves at constant velocity unless a net force acts to change its speed or direction

There are _______ equivalent ways to express Newton's
second law of motion:

– Force = mass × acceleration
– Force = rate of change in momentum

Newton's second law of motion tells us

that an object going around a curve has an acceleration pointing toward the inside of the curve

For every force, there is always

an equal and opposite reaction force

How does the force the Earth exerts on you compare with
the force you exert on the Earth?

Earth and you exert equal and opposite forces on
each other

Newton discovered

laws of motion and gravitation

Newton realized these same laws of physics were

identical in the universe and on Earth

What are Newton's three laws of motion?

1. Object moves at constant velocity if no net force is
acting.
2. Force = mass × acceleration
3. For every force there is an equal and opposite reaction
force.

Objects continue at constant velocity because of

conservation of momentum

The total momentum of interacting objects

The total momentum of interacting objects

Interacting objects exchange momentum

through equal and opposite forces

Angular momentum =

mass × velocity × radius

The angular momentum of an object

cannot change unless an external twisting force (torque) is acting on it

Earth experiences no twisting force as it orbits the Sun, so

its rotation and orbit will continue indefinitely

What Keeps a Planet Rotating and Orbiting the Sun?

Conservation of Orbital Angular Momentum

Energy makes matter _____

move

Energy is conserved, but it can:

– transfer from one object to another
– convert from one form to another

Basic Types of Energy:

• Kinetic (motion)
• Radiative (light)
• Potential (stored)

Energy can change type, but

cannot be created or destroyed

Thermal energy is related to temperature but

it is Not the same

Thermal Energy is

The collective kinetic energy of many particles (for example, in a rock, in air, in water)

Temperature is

a measure of the average kinetic energy of the
many particles in a substance

Thermal energy is a measure of

the total kinetic energy of all the particles in a substance. It therefore depends on both temperature and density

On Earth, Gravitational Potential Energy depends on:

– object's mass (m)
– strength of gravity (g)
– its height above the ground (h)

In space, an object or gas cloud has more gravitational energy when

it is spread out than when it contracts

A contracting cloud converts

gravitational potential energy to thermal energy

Mass itself is a form

of potential energy

E =

mc²

Concentrated energy can spontaneously

turn into particles (for example, in particle accelerators)

Energy can be neither

created nor destroyed

Energy can change

form or be exchanged between objects

The total energy content in an isolated system is

always the same

The universal law of gravitation:

1. Every mass attracts every other mass.
2. Attraction is directly proportional to the product of their masses.
3. Attraction is inversely proportional to the square of the distance
between their centers.

If the distance between two masses is doubled, the
gravitational force between the masses

Decreases by a factor of 4

Kepler's laws apply to all

orbiting objects, not just planets

Ellipses are not the only orbital paths. Orbits can be:

– bound (ellipses and
circles)
– unbound (parabola or hyperbola)

Because of angular momentum conservation, orbiting objects orbit around

their center of mass

m₁ * d₁ =

m₂ * d₂

Newton's laws of gravity and motion showed that the
relationship between the _____ (p) and _____ (a) of a system tells us the _____ of the system.

orbital period; average orbital distance; total mass

p =

orbital period

a =

average orbital distance (between centers)

(M₂ + M₂) =

sum of object masses

p² =

4π² / G(M₁ + M₂)

M₁ + M₂ =

4π²a³ / Gp²

the strength of gravity is

Directly proportional to the product of the masses (M × m)

the strength of gravity is Inversely

proportional to the square of the separation

How does Newton's law of gravity allow us to extend Kepler's laws?

– Applies to other objects, not just planets
– Includes unbound orbit shapes: parabola, hyperbola
– Can be used to measure mass of orbiting systems

Total orbital energy (gravitational + kinetic) stays

constant if there is no external force

Orbits cannot change

spontaneously

Total orbital energy stays

constant

what can make an object gain or lose orbital energy?

• A gravitational encounter
• Friction or atmospheric drag

If an object gains enough orbital energy, it may

escape (change from a bound to unbound orbit)

Escape velocity from Earth ≈

11 km/s from sea level (about 40,000 kilometer/hour)

Moon's gravity pulls

harder on near side of Earth than on far side

Difference in Moon's gravitational pull

stretches Earth

The Sun also has a small

tidal effect on Earth

The distance to the Sun makes the difference of force on both sides of the Earth

smaller than it is due to the Moon

Size of tides thus depends

on phase of Moon

Tidal friction gradually

slows Earth's rotation (and makes the Moon get farther from Earth)

the Moon once orbited faster (or slower);

tidal friction caused it to ''lock'' in synchronous rotation

Why Do All Objects Fall at the Same Rate?

The gravitational acceleration of an object like a rock does
not depend on its mass because M_rock in the equation for
acceleration cancels M_rock in the equation for gravitational
force.

Change in total energy is needed to

change orbit