Velocity and Acceleration Galileo began studying the motion

of freely falling objects before his telescopic observations.Found falling bodies do not fall at

constant rates, as Aristotle said, but are accelerated.○ Move faster with each passing second.

This steady increase in the velocity of a falling body by 9.8 m/s each second (9.8 m/s2) is called the acceleration of gravity, g, at Earth’s surface.○ Acceleration (a) is the change of a

body’s velocity (v) with time (t).

a = v/t

Acceleration of Gravity

Galileo also discovered acceleration does not depend on the mass (weight) of the object.Apollo 15 astronaut,

David Scott, demonstrated Galileo’s discovery by simultaneously dropping a feather and a steel geologist’s hammer.○ Fell at same rate, hit the

moon at the same time.

Along Comes Newton Isaac Newton (1643-1727)

From the work of Galileo, Kepler, and other early scientists, Isaac Newton was able to deduce three laws of motion describing any moving object.

These laws led Newton to an understanding of gravity.

Newton’s 1st Law of Motion1. An object in motion remains in motion,

and an object at rest remains at rest, unless acted upon by an outside force.

The hockey puck will remain in motion across the surface of the ice

until another force acts upon it.

Sidney Crosby (#87) will remain at rest unless another force

acts upon him.

Newton’s 1st Law of Motion Newton’s 1st Law of Motion also explains

why a projectile continues to move after all forces have been removed.Continues to move due to momentum (p), a

measure of its amount of motion.Equal to its velocity mutiplied by its mass.

ρ = mv

Paper clip tossed across the room has a low mass, therefore a low momentum.

Scalars vs. Vectors The mathematical

quantities used to describe the motion of objects can be divided into 2 categories:Scalar – quantities that

are fully described by a magnitude (numerical value) alone.

Vector – quantities that are fully described by both a magnitude and direction.

Distance vs. Displacement Distance is a scalar quantity referring to

how much ground an object has covered during its motion.

Displacement is a vector quantity referring to how far out of place an object it from its original position.

Speed and Velocity Speed is a rate of motion and does

not have a direction associated with it.

Velocity is a directed speed.

Driving a car at 65 mph speed is constant, but velocity is changing b/c your direction of motion is changing.

An object experiences a change in velocity (definition of acceleration) if its speed or direction change.Car’s 3 accelerators:

○ Gas pedal

○ Brake pedal

○ Steering wheel

Savg. = distance time

Vavg. = displacement time

Newton’s 2nd Law of Motion

2. Force equals mass multiplied by acceleration

F = ma

When Brooks Orpik (#44) checks Alexander Ovechkin (#8), the

force (F) Ovechkin gets hit with is the product of Orpik’s mass (m)

and acceleration (a).

Weight vs. Mass Weight is the force of gravity on mass.

Mass is the amount of matter (atoms and molecules) in an object.

Weight changes if gravity changes, mass does not.

Fweight = mg

Newton’s 3rd Law of Motion

3. For every action, there is an equal and opposite reaction.

As Evgeni Malkin (#71) skates, his blades are pushing against the ice

and at the same time, the ice is pushing back up

against his skates. This causes Geno to skate swiftly across the ice.

Newtonian Gravity Newton wondered if the

force holding the moon in orbit was the same force causing apples to fall.

Thought it would be weaker at greater distances assumed its strength would decrease as the square of the distance increased.

This relationship, the inverse square law, was familiar to Newton from his work on light.Proved to be correct.

Inverse Square Law Examples Compared with the strength of gravity at

Earth’s surface, how much weaker is gravity at the following distances?

5 Earth radii from Earth’s center?

7 Earth radii from Earth’s center?

2 Earth radii from Earth’s center?

Universal Law of Gravitation

Everything in the universe attracts each other through mutual gravitation.Force of gravity (F) depends on mass.

○ Larger masses have stronger gravity.

Wrote the famous formula for the gravitational force between two masses, M and m:

G = gravitational constant; 6.67 x 10-11 m3/kg•s2

r = distance between masses

ULG Example

Calculate the gravitational force between the Earth and the moon. Hint: Remember the moon is 3.84 x 105 km. from Earth.

Surface Gravity The surface gravity (g) on a particular

object may also be calculated from Newton’s Universal Law of Gravitation:

G = gravitational constant; 6.67 x 10-11 m3/kg•s2

r = distance between masses

Surface Gravity Example

Compare the force of gravity at Earth’s surface with the force of gravity at the surface of Mars.