Speed and direction

Further Mathematics · 9231

Further Mechanics

01Projectiles

Modelling motion2

Highest point and level-ground range Different heights and repeated crossings

Height and range2

Velocity and direction1

Equation of the path Targets and barriers Sloping ground and combined conditions

Trajectories and targets3

02Equilibrium of a rigid body

Moments and equilibrium2

Meaning and calculation of centre of mass Triangles and composite laminas Curved wire and sectors

Centres of mass in a plane3

Centres of mass of solids2

Centres of standard solids Joined solids and removed parts

Supported and suspended bodies2

Toppling and the contact edge Sliding or toppling first

Sliding and toppling2

03Circular motion

Circular kinematics2

Angular speed and revolutions Inward acceleration and real forces

Horizontal circles4

Friction and speed limits Conical pendulums Banked surfaces Two strings and tension limits

Vertical circles3

Energy and radial force Conditions for complete circles Turning or leaving the circle

Contact and subsequent motion3

Motion outside a sphere Projectile motion after leaving Joined arcs and choosing a method

04Hooke’s law

Elastic force models3

Length, extension and elastic force Equilibrium and unknown lengths More than one string or spring

Elastic energy1

Vertical motion and greatest speed Slack and stretched stages Horizontal motion and friction Elastic motion on a slope

Motion with elastic forces4

Geometry and linked models3

Symmetric strings and changing geometry Elastic strings in circular motion A string over a smooth pulley

05Linear motion under a variable force

Signed motion and time-dependent force2

Velocity, speed and distance Force given in terms of time

Force and position2

Force given in terms of position Turning points and limiting positions

Resistance and separable equations4

Linear resistance and terminal speed Quadratic resistance Friction, resistance and stopping Force depending on time and velocity

06Momentum

Momentum and direct collisions4

Signed momentum and a system Restitution and direct impact Reversal and unknown coefficients Kinetic energy lost in impact

Oblique collisions2

Oblique impact with a wall Oblique collisions of spheres

Successive collisions3

A wall and a second collision Three bodies on a line Successive perpendicular walls

Revision Notes Practice Questions Topical Questions Past Papers

Resources

Revision Notes Practice Questions Topical Questions Past Papers

Further Mechanics/Projectiles

Speed and direction

Contents

Further Mathematics · 9231

Further Mechanics

01Projectiles

Modelling motion2

Highest point and level-ground range Different heights and repeated crossings

Height and range2

Velocity and direction1

Equation of the path Targets and barriers Sloping ground and combined conditions

Trajectories and targets3

02Equilibrium of a rigid body

Moments and equilibrium2

Meaning and calculation of centre of mass Triangles and composite laminas Curved wire and sectors

Centres of mass in a plane3

Centres of mass of solids2

Centres of standard solids Joined solids and removed parts

Supported and suspended bodies2

Toppling and the contact edge Sliding or toppling first

Sliding and toppling2

03Circular motion

Circular kinematics2

Angular speed and revolutions Inward acceleration and real forces

Horizontal circles4

Friction and speed limits Conical pendulums Banked surfaces Two strings and tension limits

Vertical circles3

Energy and radial force Conditions for complete circles Turning or leaving the circle

Contact and subsequent motion3

Motion outside a sphere Projectile motion after leaving Joined arcs and choosing a method

04Hooke’s law

Elastic force models3

Length, extension and elastic force Equilibrium and unknown lengths More than one string or spring

Elastic energy1

Vertical motion and greatest speed Slack and stretched stages Horizontal motion and friction Elastic motion on a slope

Motion with elastic forces4

Geometry and linked models3

Symmetric strings and changing geometry Elastic strings in circular motion A string over a smooth pulley

05Linear motion under a variable force

Signed motion and time-dependent force2

Velocity, speed and distance Force given in terms of time

Force and position2

Force given in terms of position Turning points and limiting positions

Resistance and separable equations4

Linear resistance and terminal speed Quadratic resistance Friction, resistance and stopping Force depending on time and velocity

06Momentum

Momentum and direct collisions4

Signed momentum and a system Restitution and direct impact Reversal and unknown coefficients Kinetic energy lost in impact

Oblique collisions2

Oblique impact with a wall Oblique collisions of spheres

Successive collisions3

A wall and a second collision Three bodies on a line Successive perpendicular walls

Search resources

Further Mathematics · 9231

Further Mechanics

01Projectiles

Modelling motion2

Highest point and level-ground range Different heights and repeated crossings

Height and range2

Velocity and direction1

Equation of the path Targets and barriers Sloping ground and combined conditions

Trajectories and targets3

02Equilibrium of a rigid body

Moments and equilibrium2

Meaning and calculation of centre of mass Triangles and composite laminas Curved wire and sectors

Centres of mass in a plane3

Centres of mass of solids2

Centres of standard solids Joined solids and removed parts

Supported and suspended bodies2

Toppling and the contact edge Sliding or toppling first

Sliding and toppling2

03Circular motion

Circular kinematics2

Angular speed and revolutions Inward acceleration and real forces

Horizontal circles4

Friction and speed limits Conical pendulums Banked surfaces Two strings and tension limits

Vertical circles3

Energy and radial force Conditions for complete circles Turning or leaving the circle

Contact and subsequent motion3

Motion outside a sphere Projectile motion after leaving Joined arcs and choosing a method

04Hooke’s law

Elastic force models3

Length, extension and elastic force Equilibrium and unknown lengths More than one string or spring

Elastic energy1

Vertical motion and greatest speed Slack and stretched stages Horizontal motion and friction Elastic motion on a slope

Motion with elastic forces4

Geometry and linked models3

Symmetric strings and changing geometry Elastic strings in circular motion A string over a smooth pulley

05Linear motion under a variable force

Signed motion and time-dependent force2

Velocity, speed and distance Force given in terms of time

Force and position2

Force given in terms of position Turning points and limiting positions

Resistance and separable equations4

Linear resistance and terminal speed Quadratic resistance Friction, resistance and stopping Force depending on time and velocity

06Momentum

Momentum and direct collisions4

Signed momentum and a system Restitution and direct impact Reversal and unknown coefficients Kinetic energy lost in impact

Oblique collisions2

Oblique impact with a wall Oblique collisions of spheres

Successive collisions3

A wall and a second collision Three bodies on a line Successive perpendicular walls

Revision Notes Practice Questions Topical Questions Past Papers

Resources

Revision Notes Practice Questions Topical Questions Past Papers

Further Mechanics/Projectiles

Speed and direction

Contents

Further Mathematics · 9231

Further Mechanics

01Projectiles

Modelling motion2

Highest point and level-ground range Different heights and repeated crossings

Height and range2

Velocity and direction1

Equation of the path Targets and barriers Sloping ground and combined conditions

Trajectories and targets3

02Equilibrium of a rigid body

Moments and equilibrium2

Meaning and calculation of centre of mass Triangles and composite laminas Curved wire and sectors

Centres of mass in a plane3

Centres of mass of solids2

Centres of standard solids Joined solids and removed parts

Supported and suspended bodies2

Toppling and the contact edge Sliding or toppling first

Sliding and toppling2

03Circular motion

Circular kinematics2

Angular speed and revolutions Inward acceleration and real forces

Horizontal circles4

Friction and speed limits Conical pendulums Banked surfaces Two strings and tension limits

Vertical circles3

Energy and radial force Conditions for complete circles Turning or leaving the circle

Contact and subsequent motion3

Motion outside a sphere Projectile motion after leaving Joined arcs and choosing a method

04Hooke’s law

Elastic force models3

Length, extension and elastic force Equilibrium and unknown lengths More than one string or spring

Elastic energy1