Phy C Equations

Question 1

kinematics equations

Answer 1

vf-vi = at
vf^2 - vi^2 = 2aΔx
Δx = vit + 1/2at^2
Δx = 1/2(vf+vi)t

Question 2

magnitude of 3-deminsion vector

Answer 2

v = √(x^2 + y^2 + z^2)

Question 3

Fn on top of circular motion

Answer 3

mg - mv^2/r

Question 4

Fn at bottom of circular motion

Answer 4

mg + mv^2/r

Question 5

Tension force of pendulum at lowest point

Answer 5

T = mv^2/r + mg

Question 6

Elevator scale gives you:

Answer 6

normal force

Question 7

Elevator equations

Answer 7

Fn - mg = ma

Question 8

Work

Answer 8

Fdcosθ

∫F·dx

Question 9

Power

Answer 9

W/t
dW/dt
Fvcosθ

Question 10

Power (in terms of energy)

Answer 10

E/t

dE/dt

Question 11

Center of mass

Answer 11

xcom = (m1x1 + m2x2+…)/(m1+m2+…)

Question 12

acceleration of center of mass

Answer 12

Fnet = Mtotal·acom

Question 13

velocity of center of mass

Answer 13

vcom = (m1v1 + m2v2+…)/(m1+m2+…)

Question 14

Linear momentum

Answer 14

p = m·v
Fnet = dp/dt

Question 15

Impulse

Answer 15

Δp
Favg·Δt
∫F·dt
area under curve of force-time graph

Question 16

Inelastic collision

Answer 16

p1i + p2i = p1f + p2f

p1i + p2i = (m1 + m2)vcom

Question 17

Kinetic energy

Answer 17

1/2 mv^2

1/2 Iω^2

Question 18

potential energy

Answer 18

mgh

Question 19

Elastic collision

Answer 19

v1f = (m1-m2)v1i/(m1+m2) + (2m2)v2i/(m1+m2)
v2f = (2m1)v1i/(m1+m2) + (m2-m1)v2i/(m1+m2)

Question 20

conservation of momentum

Answer 20

m1v1 + m2v2 = m1v1f + m2v2f

Question 21

Scalar product

Answer 21

a·b = abcosθ

Question 22

Vector product

Answer 22

a x b = absinθ

Question 23

angular position

Answer 23

θ = s/r

Question 24

angular velocity

Answer 24

ω = θ/t = dθ/dt
v = ωr

Question 25

period

Answer 25

T = 2π/ω = 2πr/v
T = 1/f

Question 26

angular acceleration

Answer 26

α = ω/t = dω/dt
a = αr

Question 27

Rotational inertia

Answer 27

I = ∫r^2 dm
I = Σmr^2

Question 28

parallel axis theorem

Answer 28

I = Icom + mh^2

Question 29

Torque

Answer 29

τ = rFsinθ
τ = Iα
W = τθ
W = ∫τ dθ

Question 30

Power (rotational)

Answer 30

P = τω

Question 31

Angular momentum

Answer 31

L = Iω
L = r x p = rmvsinθ
Larger I = smaller ω

Question 32

Rolling without slipping

Answer 32

have friction
vcom = ωr
acom = αr
K = 1/2 Iω^2 + 1/2mv^2

Question 33

Frequency

Answer 33

cycles per second

unit: hertz, 1 Hz = 1 cycle/s

Question 34

Physical pendulum

Answer 34

T = 2π√(I/mgh)

Question 35

springs in series

Answer 35

1/keff = 1/k1 + 1/k2 +…

Question 36

springs in parallel

Answer 36

keff = k1 + k2 + …

Question 37

orbital speed

Answer 37

v = √(GM/R)

Question 38

Gravitational Potential energy

Answer 38

U12 + U13 + U23

negative (total energy also negative)

Question 39

Escape speed

Answer 39

K + U = 0

v = √(2GM/R)

Question 40

Kepler’s first law

Answer 40

Law of orbits

all planets move in elliptical orbits with the sun at one focus

Question 41

Kepler’s second law

Answer 41

Law of Areas

dA/dt is constant

Question 42

Kepler’s third law

Answer 42

T^2 = (4π^2/GM)r^3
r = semi major axis of orbit

Question 43

Gravitational kinetic energy

Answer 43

K = GMm/2r

positive number

Question 44

Electric field of Dipole

Answer 44

E = (1/2πε0) qd/z^3
E = (1/2πε0) p/z^3
p = dipole moment = qd

Question 45

Electric field of charged ring

Answer 45

E = kqz/ (z^2 + R^2)^(3/2)

Question 46

Electric field of charged disk

Answer 46

E = σ/(2ε0) (1- (z/√(z^2 + R^2)))

Question 47

Torque on dipole

Answer 47

τ = p x E = pEsinθ

Question 48

Potential energy of dipole

Answer 48

U = -pEcosθ = -p·E

Question 49

E inside sphere with uniform volume charge density

Answer 49

E = (kq/R^3)(r)

Question 50

electric potential

Answer 50

V = U/q