W2 NewtonsLawsofMotionAndGravity

Newton's Laws of Motion

• Developed by Sir Isaac Newton (1643-1727).

• Established the mathematical framework explaining the dynamics of objects, including planetary motion.

• Newton's laws are foundational to classical mechanics.

Newton's First Law

• Objects at rest stay at rest, and objects in motion continue with constant velocity unless acted upon by an external force.

• Example: Ice skating with negligible friction; a skater will glide indefinitely unless hindered by outside forces such as hitting a wall or air resistance.

Newton's Second Law

• Describes how force affects motion: Force (F) = Mass (m) x Acceleration (a).

• The acceleration of an object depends both on the force applied and its mass.

  • Higher mass = smaller acceleration for the same force.

  • Example: A heavier object (80 kg) imparts more force than a lighter one (like a table tennis ball) when colliding at the same velocity.

Newton's Third Law

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

• Explains interactions between objects during collisions and the concept of momentum.

Momentum

• Defined as Momentum = Mass x Velocity.

• Linear momentum: The typical momentum discussed in everyday circumstances.

• Angular momentum: Defined as Angular Momentum = Mass x Velocity x Radius.

• Angular momentum conservation is critical in understanding planetary motion and movements like ice skaters' pirouettes.

Conservation of Angular Momentum

• When an ice skater pulls arms in, the radius decreases, resulting in an increase in angular velocity; vice-versa when arms are extended.

• Crucial concept for explaining the motion of celestial bodies and their orbits.

Application to Celestial Objects

• Halley's Comet: Velocity changes as it orbits the sun.

  • Closer to the sun, the radius is smaller, leading to higher velocity.

  • Further from the sun, the radius is larger, lowering velocity.

• Both adjustments in velocity maintain the conservation of angular momentum.

• Kepler's laws can be derived mathematically from angular momentum conservation principles.

Stars and Angular Momentum

• As stars age, they expand while conserving angular momentum.

• Question to ponder: As a star gets bigger, what happens to its surface velocity? This highlights the importance of angular momentum in stellar evolution and dynamics.

In Summary

• Newton provided a comprehensive framework to unite the explanations of planetary movement, articulated by Kepler and observed by Tycho Brahe and Galileo.

• Understanding Newton’s laws allows us to derive Kepler’s laws and grasp the underlying physical realities governing both everyday objects and celestial phenomena.