| Quantity |
Symbol |
Formula |
| % Error |
|
% Error
= ( |A-M| ) x 100 /A |
| %
Uncertainty |
|
%
Uncertainty = (Uncertainty x 100) / Measurement |
| Distance
(Linear displacement) |
Dd |
Dd = xf - xo |
| Elapsed
Time |
Dt |
Dt = tf - to |
| Instantaneous
Speed |
V |
V = Dd / Dt
(with t approaching zero seconds) |
| Average
Speed |
Vavg |
Vavg
= (total distance traveled)/(total elapsed time) |
| Acceleration |
a |
a = DV/Dt
= (Vf - Vo) / (tf - to) |
| Final
Speed |
Vf |
Vf =
Vo + aDt |
| Original
Speed |
Vo |
Vo
= Vf - aDt |
| Elapsed
Time |
Dt |
Dt = (Vf - Vo)
/ a |
| Kinematic Equations: |
====> |
(Uniform Acceleration) |
| Final Velocity |
Vf |
Vf
= V0 + aDt |
| Displacement |
Dd |
Dd = V0Dt + 0.5(at2) |
| Final
Velocity |
Vf |
Vf2
= V02 + 2aDd |
| Displacement |
Dd |
Dd = 0.5(Vf + V0)Dt |
| Elapsed Time |
Dt |
Dt = (Vf -V0) / a |
|
|
|
| Free Fall from Rest |
Vo = 0.0 m/s |
g = -9.8 m/s2 |
| Final Velocity |
Vf |
Vf
= gDt |
| Displacement |
Dd |
Dd = 0.5(gt2) |
| Final
Velocity |
Vf |
Vf2
= 2gDd |
| Displacement |
Dd |
Dd = 0.5(Vf )Dt |
| Elapsed Time |
Dt |
Dt = (Vf) / g |
| Elapsed Time |
Dt |
Dt = Sq. root of (2d/g) |
| |
|
|
| Dynamics |
Equations |
|
| Force
(Newton's 2nd Law) |
F
= Force |
F
= ma |
| Friction |
Ff |
Ff = mFn |
| Newton's
Third Law |
. |
FAB
= -FBA |
| Weight |
Fg
= Fw |
Fg
= Fw = mg |
| Normal
Force |
Fn |
Fn = FwCos q = |
| Coefficient
of Friction |
m |
m= Ff / Fn |
| Atwood
Machine |
|
|
| Net
Force |
Fnet |
Fnet = (M1- M2)g = DMg |
| Acceleration |
a |
a
= (Fnet ) / (M1+ M2) |
| Net
Force |
Fnet |
Fnet
= (M1+ M2)a |
| Mass
1 |
M1 |
. |
| Mass
2 |
M2 |
. |
| Total
Mass |
Mtot |
Mtot
= M1+ M2 |
| Mass
Difference |
DM |
DM = M1- M2 |
|
|
|
Force and
on an |
Acceleration
incline |
|
| Angle
of Incline |
q |
q
= Sin-1(Opp/adj) |
| Acceleration
(net) |
a |
a = gsin q |
| Accelerating
Force |
Fa |
Fa
= Fw (Sin q) |
| Normal
Force |
FN |
FN = Fw (Cos q) |
| Vertical
Acceleration |
ay |
ay = gsinqsinq |
| Horizontal
Acceleration |
ax |
ax = gsinqcosq |
|
|
|
| Projectile Motion |
|
|
| (No Air
Resistance!) |
x = horizontal,
y = vertical |
(Acceleration
is in the vertical direction only!) |
| ax =
0.0 m/s2, ay = 9.8 m/s2 |
Down vectors
are negative in Value! |
Subscript
"o" means time is 0.0 seconds |
| |
Up
vectors are positive in value! |
Formulas
require ay to be positive 9.8 m/s2. (The negative value
has already been entered into the formulas for acceleration!) |
| Horizontal
Motion |
|
|
| xf = xo
+ Vxot |
Vxf = Vxo |
ax
= 0.0 m/s2 |
| Vertical Motion |
|
|
| yf = yo +
Vyot
- 0.5gt2 |
Vyf = Vyo
- gt |
V2yf = V2yo - 2gDy |
| |
|
|
| Projectile
Terms and Units: |
|
|
| xf |
Final
Horizontal Position (meters) |
Dx = xf - xo = Vxot |
| xo |
Initial
Horizontal Position (meters) |
xo
= xf - Vxot |
| Vxo |
Initial
Horizontal Velocity (m/s) |
Vxo = (xf - xo)
/ t = Vxf |
| Vxf |
Final
Horizontal Velocity (m/s) |
Vxf = Vxo
= (xf - xo) / t |
| ax
|
Horizontal
Acceleration (m/s2) |
ax
= 0.0 m/s2 |
| yf |
Final
Vertical Position
(m) |
Dy = yf - yo= Vyot - 0.5ayt2 |
| yo |
Initial
Vertical Position
(m) |
yo = yf
- Vyot
+ 0.5ayt2 |
| Vyo |
Initial
Vertical Velocity (m/s) |
Vyo = Vyf
+ ayt |
| Vyf |
Final
Vertical Velocity (m/s) |
Vyf = Vyo
- ayt |
| Dy |
Change in
Vertical Position (m) |
Dy = (yf
- yo) |
| ay
|
Earth's
Gravitational Acceleration (m/s2) |
ay = g = -9.8 m/s2 |
| t |
Time of
"flight" (s) |
t
= (Vyf - Vyo) / ay
|
| Projectile Launched |
at angle q |
from the horizontal |
| q |
Angle of Launch
from the horizontal (degrees) |
q = tan -1 (Vyo /
Vxo) |
| Vo |
Resultant
Launch Velocity |
V2o
= V2yo
+ V2xo |
| Vxo |
Horizontal
Launch Velocity (Component) |
Vxo =
Vo . Cos q |
| Vyo |
Vertical Launch
Velocity (Component) |
Vyo =
Vo . Sin q |
| R
(if, yf = yo) |
Maximum
Horizontal Distance traveled
(or Range) in meters |
R = (V2o
Sin 2q) / g |
Momentum |
(Linear) |
Units:
P = kg.m/s J = N.s |
| P |
Momentum |
P = mV |
| J |
Impulse |
J = F.t |
| DP |
Change in
Momentum |
D(mV) = m(Vf - Vo) |
| J = DP |
Impulse =
Change in Momentum |
F.t
= D(mV) |
| Ptot
= SmnVn |
Total Initial
Momentum |
m1V1
+ m2V2 + m3V3 + ..... |
| P'tot
=SmnV'n |
Total Final
Momentum |
m1V'1
+ m2V'2 + m3V'3 + ..... |
| Ptot
=P'tot |
Conservation of
Momentum |
m1V1
+ m2V2 + m3V3 + ..... = m1V'1 + m2V'2 + m3V'3
+ ..... |
Explosions and Collisions: |
Type: |
Momentum Formulas |
| |
Elastic
Collision |
m1V1
+ m2V2 = m1V'1
+ m2V'2 |
| |
Inelastic
Collision |
m1V1
+ m2V2 = (m1 + m2)V'f |
| |
Explosion |
0 = m1V'1 + m2V'2 + m3V'3
+ ..... |
Work and Energy |
(Linear
Mechanical System) |
|
| Work |
W |
W = F.d
Cos q |
| Gravitational
Potential Energy |
Ep |
Ep
= Fw(h) = mgh |
| Kinetic
Energy |
Ek |
Ek
= (0.5)mv2 |
| Work |
W |
W = DEk + DEp |
| Work |
W |
W = DEk + DEp = (0.5mv2
+ mgh)f - (0.5mv2 + mgh)i |
| Total
Energy (system) |
SE |
SE = Ek + Ep + heat |
| Conservation
of Energy |
Initial
Total Energy = (SE)i |
(SE)i = (SE)f |
| Conservation
of Energy |
Final
Total Energy = (SE)f |
or (Ek + Ep
+ heat)i = (Ek + Ep + heat)f |
