Module 1 Advanced Mechanics

Motion in Gravitational Fields
Inquiry question: How does the force of gravity determine the motion of planets and satellites?

Projectile motion


Inquiry question:
How can models that are used to explain projectile motion be used to analyse and make predictions?

Circular Motion
Inquiry question: Why do objects move in circles?

can quantitatively derive the relationships between initial velocity, launch angle, maximum height, time of flight, final velocity, launch height, horizontal range of a projectile

analyse the motion of projectiles by resolving the motion into horizontal and vertical components

can conduct a practical investigation to collect primary data in order to validate the relationships between initial velocity, launch angle, maximum height, time of flight, final velocity, launch height, horizontal range of a projectile

can solve problems, create models and make quantitative predictions by applying the equations of
motion relationships for uniformly accelerated and constant rectilinear motion

s=ut+1/2 at^2 v^2=u^2+2as
v=u+at

conduct investigations to explain and evaluate, for objects executing uniform circular motion, the
relationships that exist between:
– centripetal force
– mass
– speed
– radius

analyse the forces acting on an object executing uniform circular motion in a variety of situations,
for example:
– cars moving around horizontal circular bends
– a mass on a string
– objects on banked tracks

solve problems, model and make quantitative predictions about objects executing uniform circular motion in a variety of situations, using the following relationships

a=v^2/r
v=2pi x r/T
F=mv^2/r
w= da/dt

investigate the relationship between the total energy and work done on an object executing uniform circular motion


there is zero work done as the appide force is are right angles to it's motion

investigate the relationship between the rotation of mechanical systems and the applied torque – 𝜏=𝑟⊥𝐹=𝑟𝐹sin𝜃

predict quantitatively the orbital properties of planets and satellites in a variety of situations,
including near the Earth and geostationary orbits, and relate these to their uses

investigate the relationship of Kepler’s Laws of Planetary Motion to the forces acting on, and the
total energy of, planets in circular and non-circular orbits using:
𝑣=2𝜋𝑟/T
𝑟3/T^2=𝐺𝑀 𝑇2 4𝜋^2

investigate the orbital motion of planets and artificial satellites when applying the relationships between the following quantities:
– gravitational force
– centripetal force
– centripetal acceleration
– mass
– orbital radius
– orbital velocity
– orbital period

derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but not limited to:
the concept of escape velocity V = √2𝐺𝑀 𝑟
total potential energy of a planet or satellite in its orbit U = − 𝐺𝑀𝑚
total energy of a planet or satellite in its orbit
U + K = − 𝐺𝑀𝑚 2𝑟
energy changes that occur when satellites move between orbits


Kepler’s Laws of Planetary Motion

apply qualitatively and quantitatively Newton’s Law of Universal Gravitation to:
– determine the force of gravity between two objects 𝐹 = 𝐺𝑀𝑚 𝑟2
– investigate the factors that affect the gravitational field strength 𝑔 = 𝐺𝑀 𝑟2
– predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet