Physics 121
Exam 1 Formula Sheet
You may take this sheet into the Testing Center. You are allowed to
put additional handwritten information on this sheet if you so desire.
Conversion Factors
Mass
1 kg = 1000 g, 1 u = 1.66  10-27 kg
Length
1 m = 100 cm = 3.28 ft = 39.37 in, 1 mi = 1.61 km = 5280 ft = 1609 m
Time
1 day = 86 400 s, 1 yr = 3.156  107s
Speed
60 mi/h = 88.0 ft/s = 26.83 m/s, 100 km/h = 27.78 m/s = 62.14 mi/h
Angle
1 rev = 360° = 2π rad
Kinematic relationships valid iff a = constant:
v = v0 + at, r = r0 + v0t + ½ at2, r = r0 + ½ (v + v0)t,
vv = v0v0 + 2aΔr
For free fall with a = (0, -g), v0 = (vx0, vy0) = (v0 cos θ, v0 sin θ)
ax = 0, ay = -g, vx = vx0, vy = vy0 - gt, x = x0 + vx0t, y = y0 + vy0t - ½ gt2
Projectile motion over level terrain with negligible air resistance
Trajectory: y = (tan θ0)x – [g / (2v02cos2θ0)]x2 (a parabola)
Range: R = (v02/g) sin 2θ0, Maximum height: h = v02sin2θ0 / 2g
Speed v as a function of time: v2 = vx2 + vy2 = vx02 + (vy0-gt)2
Speed v as a function of y: v2 = v02 – 2g (y – y0)
Acceleration in Uniform Circular Motion:
ar = v2/ r, directed toward the center of the circle
Force
1 N = 0.225 lb, 1 lb = 4.45 N
Radial (centripetal) and Tangential Acceleration: a = ar + at, with
ar = v2/ r, directed toward the center of the circle,
at = dv/dt, directed toward the direction of motion
Energy
1 eV = 1.60  10-19 J, kcal = 1 Cal = 103 cal = 4.19 kJ,
1kWh = 3.6  106J = 3.6 MJ
Relative Motion: Relative velocity:
vBA = vBC + vCA, and, by induction, vBA = vBC + vCD + vDE + . . . + vXA
Relative acceleration: aBA = aBC, if aCA = 0
speed of light
gravitational constant
For Earth:
free-fall acceleration
mass
mean radius
tera- T 1012
milli- m 10-3
Physical Constants
c
2.998  108 m/s
G
6.670  10-11 Nm2/kg2
9.80 m/s2 = 32.15 ft/s2
5.98  1024 kg
6370 km
g
ME
RE
Metric Prefixes
giga- G 109 mega- M 106
micro- μ 10-6 nano- n 10-9
kilo- k 103
pico- p 10-12
Chapter 2 - Motion in One Dimension
Position: x(t)  x-coordinate at time t, y(t)  y-coordinate at time t, etc.
Average speed: average speed  total distance moved/Δt (Δt = elapsed time)
Displacement: Δx  xfinal – x initial
Average velocity: <v>  Δx/Δt

t
Velocity: v  dx/dt = slope on x(t) plot. Hence Δx = v (t ) dt
t0
Acceleration: a  dv/dt = d2v/dt2 = slope on v(t) plot.
Hence Δv =
t
 a(t )dt
t0
Kinematic relationships valid iff a = constant:
v = v0 + at, x = x0 + v0t + ½ at2, x = x0 + ½ (v + v0)t, v2 = v02 + 2a (x - x0)
Free fall:
a = -g (assuming that displacement is taken as positive upward and
ignoring air resistance and other smaller effects)
Chapter 3 - Vectors
Vector notation: A is a vector, A is its magnitude (which includes units) and
û is a unit vector in the direction of A. Hence A  Aû. The
direction of û is given by the right-hand rule.
Vector components in two dimensions: A = Axî+ Ayĵ = (Ax, Ay)
r is a position vector in two dimensions: r = xî+ yĵ = (x, y), r = (x2 + y2)½
Dot (scalar) product: AB  AB cos θ (θ is the angle between A and B)
Also A  B  Ax Bx  Ay By  Az Bz .
Cross (vector) product: AB  AB sin θ û ( û is a unit vector normal to
the plane of A and B in the direction given by the right-hand rule. )
ˆi
ˆj
kˆ
Also A  B  Ax
Bx
Ay
By
Az .
Bz
Chapter 4 - Motion in Two [Three] Dimensions
Definitions:
Position: r  (x, y, [z]) Displacement: Δr  (Δx, Δy, [Δz])
Velocity v  dr/dt = (dx/dt, dy/dt, [dz/dt]) = (vx, vy, [vz])
Acceleration: a  dv/dt = (dvx/dt, dvy/dt, [dvz/dt]) = (ax, ay, [az])
Vector Differentiation:
Rectangular form:
dV dvx ˆ dv y

i
dt
dt
dt
Polar form with v = (v, θ):
dv dv
d
 uˆ ||  v
dt dt
dt
ˆj  dvz kˆ  (a , a , a )
x y z
dt
uˆ 