PHYS 2211 Test 2 | Questions and Solutions | 2025 Update | 100% Correct –
GT.
Things you must have memorized
The Momentum Principle The Energy Principle The Angular Momentum Principle
Definitions of: velocity, momentum, particle energy, kinetic energy, work,
angular velocity, angular momentum, torque
Other useful formulas
1 2
ц Ξp E2 — (pc)2 = mc2
1 — (|~v | 2 /c 2 )
F~ grav =< 0, —mg, 0 > ∆Ugrav = mg∆y
m1 m2 m1m2
F~ g r av = G (—rˆ) U grav = —G
|~r | 2 |~r |
F~ = 1 q1q2 rˆ U = 1 q1q2
electric electric
4⇡✏0 |~r | 2 4⇡✏0 |~r |
F~ = —k (|L ~ | — L )L̂ 1 2
U kss
spring s 0 spring =
2
1 F~ n e t
~r = ~r + ~v ∆t + (∆t)2 ∆E = mC∆T
f i i thermal
2 m
d|p~ | ~ = | p~|dpˆ = | p~||~v |n̂
d p~= d| p~|
p̂ + |p~ |dpˆ F~ = pˆ and F
?
dt dt dt dt dt R
m 1 ~r 1 + m 2 ~r 2 + .. . I = m r2 + m r2 + .. .
~rcm = 1 1? 2 2?
m1 + m2 + .. .
Ktot = Ktrans + Krel Krel = Krot + Kvib
2 1 2
Krot = Lrot Krot = Iω
2I 2
~A = L
L ~ trans,A + L
~ rot ~ rot = I ω~
L
F/A ksi
Y = (macro) Y = (micro)
∆L/L d
r
ks 13.6eV
ω = EN = — where N = 1, 2, 3 .. .
m N2
The cross product
~ ~
A × B = ⟨AyBz — AzBy, AzBx — AxBz, AxBy — AyBx⟩
, Moment of inertia for rotation about indicated axis
Constant Symbol Approximate Value
Speed of light c 3 × 108 m/s
Gravitational constant G 6.7 × 10—11 N · m2/kg2
Grav accel near Earth’s surface g 9.8 m/s2
Electron mass me 9 × 10—31 kg
Proton mass mp 1.7 × 10—27 kg
Neutron mass mn 1.7 × 10—27 kg
Electric constant 1 9 × 109 N · m2/C2
4⇡✏0
Proton charge e 1.6 × 10—19 C
Electron volt 1 eV 1.6 × 10—19 J
Avogadro’s number NA 6.02 × 1023 atoms/mol
Plank’s constant h 6.6 × 10—34 J · s
h
hbar = ~ 1.05 × 10—34 J · s
2⇡
specific heat capacity of water C 4.2 J/(g · ○C)
milli m 1 × 10—3 kilo k 1 × 103
micro µ 1 × 10—6 mega M 1 × 106
nano n 1 × 10—9 giga G 1 × 109
pico p 1 × 10—12 tera T 1 × 1012
GT.
Things you must have memorized
The Momentum Principle The Energy Principle The Angular Momentum Principle
Definitions of: velocity, momentum, particle energy, kinetic energy, work,
angular velocity, angular momentum, torque
Other useful formulas
1 2
ц Ξp E2 — (pc)2 = mc2
1 — (|~v | 2 /c 2 )
F~ grav =< 0, —mg, 0 > ∆Ugrav = mg∆y
m1 m2 m1m2
F~ g r av = G (—rˆ) U grav = —G
|~r | 2 |~r |
F~ = 1 q1q2 rˆ U = 1 q1q2
electric electric
4⇡✏0 |~r | 2 4⇡✏0 |~r |
F~ = —k (|L ~ | — L )L̂ 1 2
U kss
spring s 0 spring =
2
1 F~ n e t
~r = ~r + ~v ∆t + (∆t)2 ∆E = mC∆T
f i i thermal
2 m
d|p~ | ~ = | p~|dpˆ = | p~||~v |n̂
d p~= d| p~|
p̂ + |p~ |dpˆ F~ = pˆ and F
?
dt dt dt dt dt R
m 1 ~r 1 + m 2 ~r 2 + .. . I = m r2 + m r2 + .. .
~rcm = 1 1? 2 2?
m1 + m2 + .. .
Ktot = Ktrans + Krel Krel = Krot + Kvib
2 1 2
Krot = Lrot Krot = Iω
2I 2
~A = L
L ~ trans,A + L
~ rot ~ rot = I ω~
L
F/A ksi
Y = (macro) Y = (micro)
∆L/L d
r
ks 13.6eV
ω = EN = — where N = 1, 2, 3 .. .
m N2
The cross product
~ ~
A × B = ⟨AyBz — AzBy, AzBx — AxBz, AxBy — AyBx⟩
, Moment of inertia for rotation about indicated axis
Constant Symbol Approximate Value
Speed of light c 3 × 108 m/s
Gravitational constant G 6.7 × 10—11 N · m2/kg2
Grav accel near Earth’s surface g 9.8 m/s2
Electron mass me 9 × 10—31 kg
Proton mass mp 1.7 × 10—27 kg
Neutron mass mn 1.7 × 10—27 kg
Electric constant 1 9 × 109 N · m2/C2
4⇡✏0
Proton charge e 1.6 × 10—19 C
Electron volt 1 eV 1.6 × 10—19 J
Avogadro’s number NA 6.02 × 1023 atoms/mol
Plank’s constant h 6.6 × 10—34 J · s
h
hbar = ~ 1.05 × 10—34 J · s
2⇡
specific heat capacity of water C 4.2 J/(g · ○C)
milli m 1 × 10—3 kilo k 1 × 103
micro µ 1 × 10—6 mega M 1 × 106
nano n 1 × 10—9 giga G 1 × 109
pico p 1 × 10—12 tera T 1 × 1012
