Dynamics and Relativity 2 Flashcards
work
F.s=|F||s|cos theta
i.e work is a scalar
work total
sum of all segments
w= ∫F.ds
Hooke’s Law
Fx=-kx
-ve shows F direction opposite to extension direction
power
dw/dt
w= ∫T/0 P dt
if power constant
P=wt
P=dw/dt=..
d/dt(F.s)=F.v
conservation of energy W=Fs=…
mg(y-y0)
U=mgy
work done is stored as
potential energy
ΔU+Δk=0
since ΔU=mg(y-y0), ΔK=
-mg(y-y0)
elastic potential energy
U=1/2kx^2
Wspring=
U1-U2
work done is…
independent of path taken
to get gravitational potential,
integrate force
force is rate of change of
momentum
impulse
J=FΔt (units Ns)
conservation of linear momentum
total momentum before a collision is equal to the total momentum after a collision in the absence of external forces
elastic collision
total mechanical energy conserved
inelastic collision
total mechanical energy not conserved
angular momentum cross products
L=rxp=rxmv (r is position vector ie origin to particle)
|rxp| =
rpsintheta
angular momentum is perpendicular to
both r and p
torque cross product
t=rxF
torque
rate of change of angular momentum
if fixed radius,
v=wr so k=1/2mw^2r^2
moment of intertia
sum of mr^2
k=1/2Iw^2
special relativity postulates
1.laws of physics same in all reference frames
2. c constant
inertial
not accelerating
c constant proved by
Michelson-Morely experiment, no interference between light rays so same speed
length contraction only occurs
along direction of motion
relativistic momentum
use relativistic mass
p=gamma mv
relativistic energy
E=mrelc^2
E=gamma mc^2
how photons have energy without mass
combining relativistic momentum and energy gives
E^2=m^2c^4+p^2c^2
