Table of Contents

1. Drawing motion graphs:
   1. The displacement of a moving particle.
   2. Drawing a displacement-time graph of a moving particle.
   3. Negative displacement of a displacement-time graph
   4. Motion of a ball thrown upwards.
   5. Velocity-time graphs acceleration and displacement.
   6. Displacement, velocity, acceleration time graphs
   7. Displacement vs distance on a velocity-time graph
   8. Speed from a velocity-time graph
2. Motion in a straight line with constant acceleration:
   1. Motion of a particle in a straight line part b
   2. Constant versus variable acceleration.
   3. Kinematics of a particle moving in a straight line with a constant acceleration.
   4. Kinematics: A drone moving in straight line.
   5. A particle catching up another particle
   6. Finding when one particle overtakes another particle on a straight line
   7. Finding uniform acceleration and initial velocity using simultaneous equations.
   8. Finding uniform acceleration and initial velocity using simultaneous equations.
   9. Finding uniform acceleration and initial velocity of a particle passing posts
   10. A particle moving in a straight line with constant acceleration
   11. Particles accelerating towards each other until collision
3. Vertical motion in a straight line under gravity:
   1. Throwing two balls vertically at the same instant.
   2. Distance travelled by a ball thrown vertically upwards.
   3. Throwing two balls one second apart.
   4. Throwing two particles one from ground level the other from a tower.
   5. Finding the distance between two floors by dropping a ball
4. Forces and Newton's laws of motion:
   1. Forces on a falling ladder from a brick wall.
   2. The forces on a ball in the air.
   3. Finding the tension in the couplings of a toy train
   4. Forces on a man and a lift moving upwards and downwards.
   5. Forces on a man and lift with reaction graph
   6. Forces on a man and lift with velocity-time graph
   7. Connected objects in a pulley system
   8. A pulley problem with a velocity-time graph
   9. Resolving a two pulley system.
   10. A block on a rough table connected to another block by a smooth light pulley
   11. Connected objects with vertical motion under gravity
   12. Distance of a block that comes to rest from top of a slope
   13. A box moving along a horizontal smooth and rough plane
   14. A box moving along a smooth and rough inclined plane
5. Variable acceleration:
   1. Variable acceleration introduction.
   2. Motion of a particle in a straight line part b
   3. Displacement, distance, velocity and acceleration.
   4. Using differentiation to describe the motion of a particle
   5. The distance of a particle P from the origin O.
   6. Determining whether a particle changes direction using velocity
   7. Kinematics introduction.
   8. A moving particle on a straight line.
   9. A moving particle P
   10. Kinematics variable acceleration with a piecewise function
   11. Determining the direction of two particles moving along a straight line
   12. Speeding up or down from a velocity-time graph
   13. Determining whether speed is decreasing or increasing from a velocity-time graph.
6. Projectile motion:
   1. The general equations of a projectile.
   2. A model for a projectile launched from a building.
   3. Finding the angle of projection given the range.
   4. Hitting a boat on water using projectile motion
   5. The bounding parabola for projectile motion.
   6. Projecting a particle P on a uniform slope
   7. Projecting a particle P downwards on a uniform slope.
   8. Projecting a particle P downwards on a uniform slope.
   9. Determining whether a projectile hits a wall given u and y_max
   10. The path of a cricket ball
7. Motion in two or three dimensions:
   1. Motion in two dimensions using vectors
   2. Motion in two dimensions using vectors
   3. Motion in three dimensions.
   4. Modelling the path of a hockey ball.
   5. The movement of a particle with an acceleration in the i direction
8. Force and motion:
   1. Resolving forces on a block inclined when in equilibrium
   2. The forces block suspended from P and Q and angle is 90 degrees
   3. A block suspended by a light string showing components.
   4. Finding the resultant of a system of forces.
   5. Resolving forces on a block moving up a slope.
   6. Particle on a rough slope leading to projectile motion.
   7. Which way to draw the frictional force for a block to be in equilibrium.
9. Work, energy and power:
   1. Work done against gravity.
   2. The total work done in moving a block horizontally
   3. Work done against gravity and friction.
   4. Finding velocity using the Principle of Conservation of Energy
   5. Finding height using the Principle of Conservation of Energy.
   6. The conversation of the energy of a particle moving down a slope
   7. Conservation of energy for a swing
   8. Energy gained by a block being winched up a rough slope.
   9. Finding the power of a car acending a hill with a constant velocity.
   10. The power needed by a pump raising and ejecting water.
10. Moments of forces:
    1. Introduction to moments of forces.
    2. Moments of a wooden plank supported in two places.
    3. The moment of a couple.
    4. 1st and 2nd class levers.
    5. Finding the force to keep an inclined uniform lamina in equilibrium.
    6. Resolving a ladder problem
    7. The forces of a rectangular lamina in equilibrium
11. Impulse and momentum:
    1. The principle of the conservation of momentum
    2. Conservation of momentum when two objects combine
    3. The conservation of momentum when objects are connected
    4. The collision of three particles
12. A model for friction:
    1. A model for friction.
    2. A block on a rough slope inclined at an angle theta to the horizontal.
    3. A pulley system on a rough table.
    4. Conditions for a block to slip downwards on a rough plane.
    5. A block on a rough slope using Newton 2nd law.
    6. Connected objects on a rough slope with friction
13. Centre of mass 1:
    1. The centre of gravity of a coordinate system.
    2. The centre of gravity of a rectangular lamina.
    3. Finding the centre of mass of a uniform 2D body.
    4. Finding the centre of mass metal disc with a hole.
    5. The centre of mass of a uniform triangular lamina.
    6. Sliding and toppling of a uniformed block
    7. Sliding and or toppling of a uniform block with dimensions
    8. Centre of mass: The leaning tower of Lire
14. Circular motion:
    1. Circular motion - angular speed
    2. The acceleration of a body moving with uniform motion on a circular path.
    3. A car and police car moving with the same angular speed.
    4. A model for a conical pendulum
    5. A car on a circular banked track
    6. Motion in a vertical circle.
    7. The reaction force R of a bead threaded on a smooth vertical circular wire.
    8. The motion of a particle from rest on the top of a smooth sphere.
15. Hooke's Law:
    1. Finding the extension of a particle P using Hooke's law
    2. Finding the extension of a light elastic spring by a mass on a slope.
    3. The compression of a spring after a collision.
    4. Using Hooke's law with more than one elastic string
    5. Work and energy using Hooke's law for vertical motion
    6. The mechanics of a catapult using Hooke's law
16. Differential equations:
    1. The limiting value of a differential equation 01.
    2. The limiting value of a differential equation 02.
    3. Solving a differential equation for an electrical circuit.
    4. Second order differential equations damped oscillations
    5. Non-homogeneous 2nd order differential equations
    6. Modelling a bungee jump with a 2nd order differential equation.
    7. The steady state response of a damped second-order system
    8. Solving a 2nd-order differential equation using Laplace transformations
    9. The differential equation of a damped system
    10. Damped vibrations with graphs
    11. Differential equation solution of a mass being projected upwards
    12. Solution of a 1st order differential equation with slope field.
    13. Graphical solution of a 2nd-order differential equation
17. Simple harmonic motion:
    1. Simple harmonic motion introduction.
    2. Modelling UK tides using simple harmonic motion
    3. Simple harmonic motion of a mass fixed by two elastic strings
    4. A suspended vertical spring in simple harmonic motion.
    5. Simple harmonic motion of a mass on a vertical elastic string fixed to two points
    6. Simple harmonic motion as a function of time
18. Centre of mass 2:
    1. The centre of gravity of combined hemisphere and cone.
    2. Volume of revolution introduction.
    3. Finding the centre of mass for a uniform 3D mass.
    4. Finding the centre of mass of a solid hemisphere of radius r
    5. Finding the centre of mass of a solid cone radius r, height h.
    6. Finding the centre of mass of a hollow bowl.
    7. Finding the centre of mass of a lamina plane introduction.
    8. The centre of mass of a lamina bounded by a quadratic, x = a and x = b
    9. The centre of mass of a lamina between two curves.
    10. Centre of gravity of a solid of revolution
19. Oblique impacts:
    1. The ideal squash serve
    2. Oblique impacts
    3. The oblique impact of two balls.
    4. Oblique impact of smooth elastic spheres using motion along the line of centres.
    5. Oblique impact of two smooth balls with movable point of contact.
    6. Modelling oblique collisions using a matrix.