Physics 4: Mod 1 - Further Mechanics

Physics 4: Mod 1 - Further Mechanics

1. Momentum Concepts

   • Force as the rate of change of momentum
     • F=\(\frac{\Delta(mv)}{\Delta(t)}\)
   • Impulse
     • F\(\Delta\)t = \(\Delta\)(mv)
   • Area under force time graph
   • Conservation of linear momentum
   • Elastic and inelastic collisions
     • Explosions

2. Circular Motion

   • Circular path at constant speed means acceleration
   • Centripetal force
     • F=\(\frac{mv^2}{r}\) = m\(\omega^2\)r
   • Angular speed
     • \(\omega\) = \(\frac{v}{r} = 2\pi\)f
   • Centripetal acceleration
     • a = \(\frac{v^2}{r}\) = \(\omega^2\)r

3. Simple Harmonic Motion

   • Characteristic features
   • Conditions
   • Equations
     • a = \[-(2\pi\f)^2\]x
   • Graphs
     • Significance of gradients
   • Max speed
   • Max acceleration

4. Simple Harmonic Systems

   • Mass-spring system
     • T=2\(\pi\) \(\sqrt\frac{m}{k}\)
   • Simple pendulum
     • T=2\(\pi\) \(\sqrt\frac{l}{g}\)
   • Energy considerations
     • Kinetic energy
     • Potential energy
     • Variations with displacement
     • Variations with time

5. Forced vibrations and resonance

   • Free and forced
   • Resonance
   • Damping
   • Phase difference and drivers
   • Examples in mechanical systems
   • Stationary waves