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