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Further Mechanics

Name Definition Formulae
                                                                        MOMENTUM
Momentum p=mv
Impulse Change in momentum I=FDelta t=Delta p
Newton’s second Law F_{resultant}=frac{d}{dt}(p_{total})

F_{resultant}=frac{d}{dt}(mv)
if m=const F_{resultant}=mfrac{dv}{dt}=ma
if mneq const,v=const F_{resultant}=vfrac{dm}{dt}
mneq const,vneq const F_{resultant}=mfrac{dv}{dt}+vfrac{dm}{dt}
if E_{r}=0 P_{resultant} =0
Conservation of
momentum		 The total momentum before a collision is the same as total
momentum after collision
(provided that there is no external force acting on the
system)		 p_{initial}=p_{final}
Elastic collision KE is conserved (e.g. Identical masses move apart at 90°)
Inelastic collision KE is not conserved (e.g. explosions, stick after collision)
                                                                                             CIRCULAR MOTION
Angular velocity v=wr

w=frac{2Pi }{T}
Centripetal
acceleration		 a=frac{v^{2}}{r}=w^{2}r
Centripetal force A resultant force is required to produce and maintain
circular motion		 F=ma=frac{mv^{2}}{r}=mw^{2}r
Weightlessness No reaction forces
For astronauts on ISS, gravitational force = centripetal force,
hence no reaction force