Download AP Physics Chapter 2-4 Key Equations and Ideas Vectors (dot

AP Physics Chapter 2-4 Key Equations and Ideas
Vectors
 
a  b  (ax  bx )î  (ay  by )ĵ  (az  bz )k̂
 
a  b  ab cos   ax bx  a y by  az bz (dot product)
 
a x b  ab sin 
ĵ
î
k̂
î ĵ k̂
a y az
ax a y
ax az
 
a x b  ax a y az 
î 
ĵ 
k̂  ( a y bz  az by ) î  ( ax bz  az bx ) ĵ  ( ax by  a y bx ) k̂
by bz
bx bz
bx by
bx by bz
 
Direction of a x b (vector product) is determined by the right-hand rule
î x ĵ  k̂
ĵ x k̂  î
k̂ x î  ĵ
ĵ x î   k̂
k̂ x ĵ   î
î x k̂   ĵ
y
2-D
x = r cos 
y = r sin 

1-D
Acceleration
y
 = tan-1 x

x
x
x2 – x1


r2 - r1
x
 v dt
 area under vt graph

dy
dr dx
dz

î 
ĵ 
k̂
dt dt
dt
dt
v
 a dt
 slope on xt graph
 area under at graph
x
t
dx
vinst 
dt
v
a avg 
t
dv
ainst 
dt
v avg 
Velocity
x2  y 2
3-D

r  x î  yĵ  zk̂
Position
Displacement
r


r
Comments
r

dvy
dv
dv dvx

î 
ĵ  z k̂
dt
dt
dt
dt
x2  y 2  z2
 slope on vt graph
Projectiles
Kinematic Equations
x = vx0t = (v0cos 0)t
(constant accel)
y = vy0t – ½gt2 = (v0sin 0)t - ½gt2
2
xf = xi + vit + ½at
vf = vi + at
For symmetric projectiles
v
TMaxHeight  o sin o
g
vf2 = vi2 + 2a(xf – xi)
xf = xi + ½(vf + vi)t
Uniform Circular Motion
v2
r
d 2r
T=

v
v
ac 
Fc  mac  m
r
ac
v
v2
r
v2
R  xMax  o sin 2 o
g
TTotal 
2vo
sin  o
g
v 2yo
H  yMax 

2g
(vo sin  o )2
2g
Key Ideas:

Use dimensional analysis (also called the factor-label method or chain-link conversions) to
convert from one unit to another. This is the sequential application of conversion factors
expressed as fractions and arranged so that any dimensional unit appearing in desired set
of dimensional units is obtained.

Use significant figures in your calculations. Keep a couple of extra significant figures in
the interim steps. Do not round until the final answer.

The order of magnitude is the power of ten when the number is expressed in scientific
notation.

Carry the units in each problem. This will serve as a check when you get to the final
answer. Always use (or convert to) SI units.

If the signs of the velocity and acceleration of an object are the same, the speed will
increase. If the signs are opposite, the speed decreases.

Is your answer sensible? Think about the reasonableness of your answer.

If the angle between two vectors is 0o, the dot product is a maximum. If the angle is 90o,
the dot product is zero.

If the angle between two vectors is 0o, the vector (cross) product is zero. If the angle is
90o, the vector product is a maximum.

When determining the angle between two vectors, they must be arranged tail-to-tail.

To determine the direction of the resultant vector of a vector product, use the right-hand
rule and sweep the first vector into the second vector. Your thumb will determine the
direction of the resultant vector.

The direction of the instantaneous velocity of an object is always tangent to the path of
the object’s position.

In projectile motion, the horizontal motion and the vertical motion are independent of one
another. Neither motion affects the other.

Solve a problem as far as you can algebraically (i.e. with letters and symbols). Substitute
in numbers in the final step.