Physics I. Formula Sheet
Right triangle:
sin
= a/c
cos
= b/c
tan
= a/b
c
2
= a
2
+ b
2
Quadratic Formula:
Ax
2
+ Bx + C = 0 has solutions:
Misc Formulas:
Circumference of a circle = 2R
Area of a circle = R
2
Surface Area of a Sphere = 4R
2
Volume of sphere = (4/3)R
3
Volume of cylinder = R
2
L
Differentiation:
dx
n
/dx = nx
n-1
(n ≠ 0)
dcos(x)/dx =
sin(x) (x in radians)
dsin(x)/dx = cos(x) (x in radians)
d(f(x) + g(x))/dx = df(x)/dx + dg(x)/dx
Integration:
1-D Motion:
displacement = x
v
average
:
x/
t = (x
2
– x
1
)/(t
2
– t
1
)
a
average
:
v/
t = (v
2
– v
1
)/(t
2
– t
1
)
Given x(t)
v(t) = dx/dt (instantaneous)
a(t) = dv/dt = d
2
x/dt
2
(instantaneous)
1-D Motion with Const. Acc.:
x(t) = x
0
+ v
0x
t + (1/2) at
2
v(t) = v
0
+ at
v
2
= v
02
+ 2a(x – x
0
)
Projectile Motion:
x(t) = x
0
+ v
0x
t
v
x
(t) = v
0x
a
x
(t) = 0
y(t) = y
0
+ v
0y
t + (1/2) a
y
t
2
v
y
(t) = v
0y
+ a
y
t
a
y
(t) = a
y
Acceleration due to gravity:
g = 9.8 m/s
2
downward
Equations connect. trans./rotat. motion
v
tan
= R
a
tan
= R
Rotat. kinematic eq-ns with const.
angular acceleration
(t) =
0
+
t
(t) =
0
+
0
t +(1/2)
t
2
2
0
2
+ 2
(
–
0
)
Centripetal acceleration:
a
r
= v
2
/R; a
R
=
2
R
Newton 2
nd
law
Friction Forces:
Fs ≤ µsN
Fk = µ
k
N
Work and Kinetic Energy
∙
K = (1/2)mv
2
Wnet = K
K = K
f
K
i
Potential Energy:
For gravity on earth's surface:
F=mg
U(y) = U
0
+ mgy
For a spring:
F = kx
U(x) = (1/2)kx
2
2
With conservative forces only:
E
tot
= K + U
With non-conservative forces:
Power
P
avg
= W/t
P = dW/dt
P
F
v
∙
cos
∙
A
ACBB
x2
4
2
C
n
x
dxx
n
n
1
1
