Module 5: Advanced Mechanics

HSC Physics 2026: recall practice based on the 2017 syllabus.

In the ideal projectile model what horizontal acceleration acts?

Zero horizontal acceleration.

In the ideal projectile model what vertical acceleration acts?

Downwards at constant g.

How do horizontal and vertical components of projectile motion interact?

They are independent but share the same flight time.

For launch speed u at angle θ above horizontal what is initial horizontal velocity?

u cos θ.

For launch speed u at angle θ above horizontal what is initial vertical velocity?

u sin θ.

At a projectile's maximum height what is its vertical velocity?

Zero instantaneously.

At a projectile's maximum height what is its acceleration?

Downwards at g.

For a projectile returning to launch height how do ascent and descent times compare?

They are equal in the ideal model.

For a projectile returning to launch height how does landing speed compare with launch speed?

They are equal without air resistance.

For ideal projectiles launched and landing at the same height which angle maximises range?

45° above horizontal.

For equal launch speeds and equal launch and landing heights what is true of complementary launch angles?

They produce equal ranges without air resistance.

How do you find projectile flight time when launch and landing heights differ?

Solve the vertical displacement equation for time.

How do you find a projectile's horizontal range after finding flight time?

Multiply constant horizontal velocity by flight time.

What is the direction of instantaneous velocity in circular motion?

Tangential to the circular path.

What is the direction of centripetal acceleration?

Towards the centre of the circle.

What is centripetal force?

The net inward force required for circular motion.

What provides the centripetal force for a car on a level bend without skidding?

Static friction between tyres and road.

What provides centripetal force for a mass whirled on a horizontal string?

The inward component of tension.

At fixed radius and mass how does centripetal force change if speed doubles?

It quadruples.

At fixed speed and mass how does centripetal force change if radius doubles?

It halves.

Which supplied equation relates circular speed to radius and period?

v = 2πr/T.

Which supplied equation gives centripetal acceleration?

a_c = v²/r.

Which supplied equation gives the required net inward force?

F_c = mv²/r.

Why can an object accelerate while moving at constant speed in a circle?

Its velocity direction changes continuously.

What work does the net centripetal force do in uniform circular motion?

Zero: force is perpendicular to displacement.

How does kinetic energy change in uniform circular motion?

It remains constant.

On a frictionless banked curve which force supplies the inward component?

The normal force.

What is torque?

The turning effect of a force about an axis.

Which supplied equation gives torque magnitude for force F at radius r?

τ = rF sin θ.

What angle in τ = rF sin θ is used?

The angle between radius vector and force.

What is the SI unit of torque?

Newton metre (N m).

How does Newton's gravitational force depend on separation?

It varies inversely with separation squared.

How does gravitational force depend on the two masses?

It is proportional to their product.

What direction does gravitational force between two masses act?

Along the line joining their centres, attractively.

In F = GMm/r² what does r represent for spherical bodies?

The distance between their centres.

What is gravitational field strength at a point?

Gravitational force per unit mass there.

How does gravitational field strength vary with distance from a spherical mass?

It varies as 1/r² outside the mass.

Why do objects of different mass have the same gravitational acceleration in a vacuum?

Gravitational force and inertial mass scale equally.

What supplies centripetal force for a satellite in free circular orbit?

Gravity.

How does circular orbital speed change as orbital radius increases around the same mass?

It decreases, proportional to 1/√r.

How does circular orbital period change as orbital radius increases around the same mass?

It increases, proportional to r^(3/2).

Which mass does ideal circular orbital speed around a planet depend on?

The central planet's mass, not the satellite's mass.

What orbital period must a geostationary satellite have?

One sidereal day, about 23 h 56 min.

What orbital plane and direction are required for a geostationary satellite?

Circular equatorial orbit in Earth's rotation direction.

Why are geostationary satellites useful for communications?

They remain above approximately the same ground location.

What is Kepler's first law?

Planets follow ellipses with the Sun at one focus.

What does Kepler's second law say about equal time intervals?

The Sun–planet line sweeps out equal areas.

Where is a planet fastest in an elliptical orbit?

At perihelion, closest to the Sun.

What does Kepler's third law relate for bodies orbiting the same mass?

Period squared is proportional to semi-major axis cubed.

With zero potential energy at infinity what sign is gravitational potential energy at finite radius?

Negative.

Which supplied equation gives gravitational potential energy outside a spherical mass?

U = −GMm/r.

What is the total mechanical energy of a satellite in a circular orbit?

−GMm/(2r).

What is the kinetic energy of a satellite in a circular orbit?

GMm/(2r).

What minimum total mechanical energy permits ideal escape to infinity?

Zero, with zero speed at infinity.

How does escape speed depend on the mass of the escaping object?

It is independent of that mass in the ideal model.

Which equation gives ideal escape speed from radius r around mass M?

v_esc = √(2GM/r); not directly supplied.

How does total mechanical energy change when a satellite moves to a higher circular orbit?

It increases and becomes less negative.

How does speed change after a satellite reaches a higher circular orbit?

Its new circular orbital speed is lower.

What must be checked when using the constant-acceleration equations?

Acceleration is constant over the interval.

In a projectile investigation which measurements can test a predicted trajectory?

Horizontal and vertical position at known times.

What does the gradient of a velocity–time graph represent?

Acceleration.

What does the area under a velocity–time graph represent?

Displacement.

How can a circular-motion experiment test the speed dependence of centripetal force?

Hold mass and radius constant; compare force against speed squared.

What angular speed corresponds to one revolution in period T?

ω = 2π/T.

In a banked-road force diagram which component of normal force helps turn the car?

The horizontal component towards the curve's centre.

Why does a satellite remain in orbit despite gravitational attraction?

Its tangential velocity makes it continually fall around Earth.

How does Kepler's second law relate to angular momentum?

Equal areas in equal times reflect conserved orbital angular momentum.

In an ideal elliptical orbit what happens to total mechanical energy?

It remains constant while kinetic and potential energies exchange.

What is the gravitational potential energy change when a satellite moves outward?

It increases, becoming less negative.