Gravitation and Circular Motion

Gravity

Bg:

  • Fg = mg

  • Acceleration due to gravity on Earth = 9.8 m/s²

  • Pointed down

  • Field force = applied equally across surface

    • described by vector field (vector arrows w/ direction and magnitude)

    • Field models are useful for describing interactions at a distance

  • Pulls towards the center of mass

  • All objects with mass have a gravitational pull

Law of Gravitation: gravitational force describes the interaction between multiple objects with mass

  1. Gravitational force is always attractive

  2. Gravitational force is measured from from the center of one object to another ( r )

University Law of Gravitation

  • Force of Gravity is inversely proportional to distance² between two objects’ center of mass

    • gets weaker further apart, stronger the closer

    • gravitational pull is directly proportional to mass

Universal Gravitational Constant

Newton’s Third Law: equal and opposite reaction —> forces applied are equal regardless of mass

  • Fnet = FBS - FBA

    • Facing opposite directions (Planet A and Star’s forces of gravity to Planet B) so subtract

    • If the same way, add

Time

  • direct relationship with height

  • indirect relationship with radius and mass

Singular Planet

  • g = Fnet = m

  • if regarding an object above the earth’s surface, add altitude and radius of earth together for r

Circular Motion
notice how acceleration is kind of one step ahead of the velocity? cause it changes the velocity

Tangential Speed: “linear” speed of an object in circular motion ( m/s /)

  • linear speed if it were to continue moving in said straight line tangent to the circle

  • Distance/Time —> Circumference/Period

Centripetal Acceleration (m/s²)

  • even if constant speed, an object in circular motion is always accelerating

  • centripetal acceleration is always pointing to center

  • R- radius. v- velocity

  • object must have net force to accelerate

Centripetal Force: the center-seeking net force

  • w/o, the object would just travel straight

If an object suddenly breaks from the circcle (ex. string breaks)

  • Position moves tangentially from point P

  • Velocity is decreasing as it moves upward (acceleration and movement opposite), then when it reaches maximum height and begings to increase as it moves downward

  • Acceleration: constant, due to gravity

Circling around table horizontally: friction (and normal and gravity but cancels out)

  • solve for friction compoentns

Circling around with string: tension and gravity

Circling around like rollercoaster: normal force and gravity

Period and Frequency

Period or T ( s )

  • amount of time it takes for an object to complete one full revolution

Frequency (hertz , revolutions/time)

  • amount of revolutions per time