Mathematics: Mechanics 2

Attachments:

• Mechanics 2: Centre of Mass
• Mathematics: Mechanics 2 (Notes 1 of 2)

1. Identify position using symmetry
2. Determine position of centre of mass of a composite body
3. The effect of gravity is equivalent to a single force acting at the centre of mass
4. Use given information about the position of the centre of mass (in formula book)

1. Equilibrium means
   1. The vector sum of the forces is zero
   2. AND the sum of the moments of the forces about any point is zero
2. Solve problems including toppling and sliding
3. Calculate the moment of a force

1. Use equations of motion (horiz and vert) to solve problems
   1. Finding range on a horizontal plane
   2. Finding greatest height
   3. Magnitude and direction of velocity at a point
2. Derive and use the equation of trajectory of a projectile
3. Model the motion as a particle with constant acceleration
   1. Understand assumptions made

1. Solve problems involving a particle moving in a horizontal circle
2. Acceleration and force of a particle moving in a circle with constant speed is towards the centre of the circle

   Annotations:

   • a=r\(\omega^2\) a=\(\frac{v^2}{r}\)
3. Understand angular speed

   Annotations:

   • v=r\(\omega\)

1. Newton's experimental law
   1. Two smooth spheres
   2. Smooth sphere and surface
2. Define coefficient of restitution
   1. Perfectly elastic e=1
   2. Inelastic e=0
3. Impulse as change in momentum
   1. Using momentum = mv only

1. Work done by a force = force x distance moved PARALLEL to force
2. Gravitational potential energy
3. Kinetic energy
4. Relationship between the change in energy of a system and the work done by external forces
   1. Use conservation of energy rule
5. Define power as rate at which work is done
   1. Power = force x velocity
6. Solve problems including work done by resistance