# Year 12 – Advanced Mechanics

###### Projectile motion

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

Students:

• analyse the motion of projectiles by resolving the motion into horizontal and vertical components, making the following assumptions:
• a constant vertical acceleration due to gravity
• zero air resistance
• apply the modelling of projectile motion to quantitatively derive the relationships between the following variables:
• initial velocity
• launch angle
• maximum height
• time of flight
• final velocity
• launch height
• horizontal range of the projectile (ACSPH099)
• conduct a practical investigation to collect primary data in order to validate the relationships derived above
• solve problems, create models and make quantitative predications by applying the equations of motion relationships for uniformly accelerated and constant rectilinear motion

Resource – Projectile Motion – 2 Pages

###### Circular Motion

Inquiry question: Why do objects move in circles?

Students:

• conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationship that exist between:
• centripetal force
• mass
• speed
• 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 (ACSPH100)
• solve problems, model and make quantitative predictions about objects executing uniform circular motion in a variety of situations, using the following relationships
• $\vec{a} = \frac{\lvert{\vec{v}}\rvert^{2}}{\vec{r}}$
• $\sum{\vec{F}} = \frac{m\lvert{\vec{v}}\rvert^{2}}{\vec{r}}$
• $\omega = \frac{\Delta\theta}{t}$

Resource – Circular Motion – Concepts – 1 Page

•
• investigate the relationship between the total energy and work done on an object executing uniform circular motion
• investigate the relationship between the rotation of mechanical systems and the applied torque $(\tau = \vec{r}\vec{F}_{\perp} = \lvert\vec{r}\rvert\lvert\vec{F}\rvert\sin{\theta})$

Resource – Circular Motion – Energy and Work – 2 pages

Resource – Circular Motion – Rotation and Torque – 2 pages

###### Motion in Gravitational Fields

Inquiry question: How does the force of gravity determine the motion of planets and satellites?

Students:

• apply qualitatively and quantitatively Newton’s Law of Universal Gravitation to:
• determine the force of gravity between two objects $(\vec{F} = -\frac{GMm}{\vec{r}^2})$
• investigate the factors that affect the gravitational field strength $(\vec{g} = \frac{GM}{\vec{r}^2})$

Resource – Gravitational Motion 1 – 2 Pages

• predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet (ACSPH094, ACSPH095, ACSPH097)
• 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 velocity
• orbital period
• 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 (ACSPH101)
• 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: (ACSPH101)
• ${v_o} = \frac{2\pi r}{T}$
• $\frac{r^3}{T^2} = \frac{GM}{4\pi^2}$
• 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 $(v_{esc} = \sqrt{\frac{2GM}{r}})$
• total potential energy of a planet or satellite in its orbit $(U = -\frac{GMm}{r})$
• total energy of a planet or satellite in its orbit $(E = - \frac{GMm}{2r})$
• energy changes that occur when satellites move between orbits (ACSPH096)
• Kepler’s Laws of Planetary Motion (ACSPH101)

Resource – Gravitational Motion 2 – 1 Page