GRAVITY AND MOTION

Kepler's Law of Planetary motion

1st Law: Law of orbits: all planets move about the sun in elliptical orbits, having the sun as one of their foci

2nd Law: the law of areas: a radius vector joining any planet to the sun sweeps out equal areas in equal lengths of time

3rd Law: the law of period

Projectile motion

Equations

initial horizontal velocity Ux = U cos theta

initial vertical velocity Uy = U sin theta

final vertical velocity
Vy = gt + Uy
Vy2 = 2gSy + Uy2

horizontal range Sx = Uxt

Horizontal projection

Vx = Ux i.e. Horizontal component of the velocity is constant

free fall vs horizontal projection: time taken to reach the ground is exactly the same

Projection at an angle

Case 1: Landing at the same height as at launch

impact velocity is the same as the initial (launch) velocity

Total hang time is twice the time taken to reach max ht
Sy = 0

Case 2: Landing at a lower height than launch

Sy is some -ve quantity

Case 3: Landing at a higher height than launch e.g. basketball

Sy is some positive quantity
i.e. Sy =3.1 - 1.6 = +1.5m

Newton's Law of Universal Gravitation

aka the inverse square law

Gravitational field strength at any height

G is the universal gravitational constant

*r is measured from the centre of the planet

Circular motion

Centripetal acceleration is directed towards the centre

Centripetal force is directed towards the centre

Tangential velocity (direction is at a tangent to the circular path at that moment)

Inclined planes

the vertical component of the force is equal to the normal force

the sliding force is the force parallel to the plane