Phys1001 Physics 1 (Regular) Formula Sheet Page 2
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1
2
3CC1529
Semester 1, 2015
Page 2 of 3
Work and Energy
Rotational Motion
1
1
dθ
2
2
K =
mv
,
U
= mgy,
U
=
kx
ω
=
,
v = rω
grav
el
z
z
2
2
dt
2
F =
kx
dω
d
θ
z
α
=
=
z
2
dt
dt
W
= K
K
= ∆K
2
1
tot
2
v
dv
dω
2
W = F s = F s cos φ
a
=
= ω
r,
a
=
= r
= rα
rad
tan
z
r
dt
dt
P
P
2
2
2
I
= I
+ M d
,
v
= Rω
W =
F cos φ dl =
F d l
P
cm
cm
P
P
2
2
2
1
1
I = m
r
+ m
r
+ . . . =
m
r
1
2
i
1
2
i
∆W
P
=
i
av
∆t
τ = rF sin θ,
= r
F
dW
P =
= F v
d L
dt
τ
= Iα
,
=
z
z
W
=
∆U
,
W
=
∆U
dt
el
el
grav
grav
1
1
E = K + U
2
2
K =
M v
+
I
ω
,
P = τ
ω
z
z
cm
cm
z
2
2
∆E = W
other
θ
1
1
2
2
2
W =
τ
dθ,
W
=
Iω
Iω
z
tot
2
1
2
2
θ
1
L = r
p = r
mv (particle)
Periodic Motion
L = I
(rigid body)
2π
ω
1
ω = 2πf =
,
f =
=
T
2π
T
k
κ
ω =
,
ω =
Moments of inertia
m
I
1
g
mgd
2
Thin rod, axis through centre:I =
M L
ω =
,
ω =
12
L
I
1
2
Thin rod, axis through one end:I =
M L
F
=
kx
x
3
x = A cos(ωt + φ)
1
2
2
Rectangular plate, axis through centre:I =
M (a
+ b
)
1
1
1
12
2
2
2
E =
mv
+
kx
=
kA
= constant
x
1
2
2
2
2
Thin rectangular plate, axis along edge:I =
M a
3
2
k
b
(b/2m)t
x = Ae
cos ω t,
ω =
1
2
2
2
m
4m
Hollow cylinder:I =
M (R
+ R
)
1
2
2
b
= 2 k m
critical
1
2
Solid cylinder:I =
M R
F
max
2
A =
2
2
Thin-walled hollow cylinder:I = M R
2
2
2
(k
mω
)
+ b
ω
d
d
2
2
Solid sphere:I =
M R
5
2
2
Thin-walled hollow sphere:I =
M R
3
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