The History of Astronomy

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Think critically about Kepler’s Laws: Would you categorize his achievements as physics or mathematics?

Mathematics

Physics

Slide 28

Isaac Newton (1643 - 1727)

Major achievements:

Invented Calculus as a necessary tool to solve mathematical problems related to motion

Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler

Discovered the three laws of motion

Discovered the universal law of mutual gravitation

Slide 29

Newton’s Laws of Motion (I)

A body continues at rest or in uniform motion in a straight line unless acted upon by some net force.

An astronaut floating in space will float forever in a straight line unless some external force is accelerating him/her.

Slide 3

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

a = Dv/Dt

Velocity and acceleration are directed quantities (vectors)!

a

v

Slide 31

Which of the following involve(s) a (non-zero) acceleration?

Increasing the speed of an object.

Braking.

Uniform motion on a circular path.

All of the above.

None of the above

Slide 32

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

Acceleration in the conventional sense (i.e. increasing speed)

a = Dv/Dt

Different cases of acceleration:

Velocity and acceleration are directed quantities (vectors)!

Change of the direction of motion (e.g., in circular motion)

Deceleration (i.e. decreasing speed)

a

v

Slide 33

A ball attached to a string is in a circular motion as shown. Which path will the ball follow if the string breaks at the marked point?

1)

2)

3)

4)

5) Impossible to tell from the given information.

Slide 34

Newton’s Laws of Motion (II)

The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force.

a = F/m  F = m a

Slide 35

Newton’s Laws of Motion (III)

To every action, there is an equal and opposite reaction.

The same force that is accelerating the boy forward, is accelerating the skateboard backward.