3
PHYS1121/PHYS1131 – FORMULA AND DATA SHEET
This information will be provided to students in a ll examination s in the course.
The symbols in formulæ have the conventional meanings.
• Kinematics
Constant acceleration: x = xo + vxot +
!
1
2
axt2
v = vxo + axt
vx2 = vxo2 + 2ax(x – xo)
Circular motion: v = rω ac = v2/r
• Dynamics
Newton’s 2nd law ΣF = dp
dt ΣF = ma
Hooke’s law F = – kx
Work dW = F.dx
Power P =
!
dW
dt
= F v cos θ
Kinetic Energy K =
!
1
2
mv2
Potential Energy U(x) = –
!
Fdx
"
F = –
!
dU
dx
U = mgh, U =
!
1
2
kx2
Momentum p = mv
Centre of mass rcm = Σmiri
M or =
⌡
⌠rdm
M
• Rotational dynamics:
ω =
!
d"
dt
α =
!
d"
dt
τ = r F sin θ = Iα
I =
!
mi
i
" ri
2
or = ⌡
⌠r2dm
L = r x p
L = mr v sin θ or = Iω
W = ⌡
⌠ τ dθ
K =
!
1
2
Iω2
!
I=2
5
MR2 solid sphere
• Thermal Physics:
ΔL
L = α ΔT
ΔV
V = βΔT
!
Q=mc "T
Q = mL
PV = nRT = NkBT
!
" = 3
2
kBT=1
2
mv2
U = N ε
_
= 3
2 NkBT
PVγ = constant
H = κA
!
dT
dx
dW = -P dV
!
"Eint =Q+W
• Gravitation
Gravitation |F| =
!
Gm1m2
r2
U = –
!
Gm1m2
r
Keppler’s 2nd Law
!
dA
dt =L
2M "
Keppler’s 3rd Law
!
T2=4"2
GM s
#
$
%
&
'
(
a3
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