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all the formulas i could think of for the ap physics 1 exam + units

1

kinematic equation #1 (vf=)

vf=vi+at

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2

kinematic equation #2 (vf²=)

vf²=vi²+2aΔx

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3

kinematic equation #3 (Δx=)

Δx=vit+1/2at²

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4

kinematic equation #4 (Δx=)

Δx=1/2(vi+vf)t

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5

displacement (d)

d=vt

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6

velocity (v)

v=Δx/t

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7

acceleration (a)

a=v/t

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8

Net Force (ΣF, newton’s second law)

ΣF=ma

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9

static friction (f_{s})

f≤μF_{n}

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10

kinetic friction (f_{k})

f=μF_{n}

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11

Universal law of gravitation (Fg=)

Fg=G(m1m2/r²)

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12

surface gravity of a planet (not earth)

g=GM/R²

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13

θ(rad)

arclength/rad

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14

convert to Δθ

Δx/r

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15

convert to ω

v/r

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16

convert to α

a/r

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17

angular velocity (ω)

ω=2π/T

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18

tangential velocity (v_{T})

2πr/T

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19

centripetal acceleration (a_{c})

a_{c}=v²/r

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20

tangential acceleration

a_{t}=rα

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21

total acceleration

a_{tot}=√ac²+at²

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22

circular net force

ΣF=mv²/r

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23

gravitational force between two objects

F=GMm/r²

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24

orbital velocity

v=√GM/r

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25

spring force equation (F_{s})

F_{s}=-kx

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26

kinetic energy

KE=1/2mv²

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27

gravitational potential energy

U_{g}=mgh

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28

Net Work (W_{net})

W_{net}=ΔK=1/2mvf²-1/2mvi²

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29

spring potential energy (U_{sp})

U_{sp}=1/2kx²

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30

power

P=W/t

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31

work (W)

W=F∥Δx

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32

avg speed

avg d/avg t

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33

average velocity

Δx/Δt

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34

instantaneous velocity

Δx/Δt (where t gets infinitely small)

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35

weight (Fg)

Fg=mg

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36

instantaneous angular speed

ω=Δθ/Δt (where t gets infinitely small)

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37

average angular speed

ω=Δθ/Δt

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38

Kepler’s Law

T²=(4π²/GM)r³ » T²∝r³

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39

find net force using momentum

ΣF=Δp/Δt

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40

impulse/change in momentum (impulse-momentum theorum)

Δp=ΣFΔt

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41

law of conservation of momentum

m_{A}v_{Ai}+m_{B}v_{Bi}=m_{A}v_{Af}+m_{B}v_{Bf}

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42

recoil collision (begin together, move apart)

m_{A}v_{Af}=-m_{B}v_{Bf}

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43

perfectly inelastic collision (begin apart, stick together)

m_{A}v_{Ai}+m_{B}v_{Bi}=(m_{A}+m_{B})v_{f}

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44

elastic collision (objects collide but dont lose KE)

v_{Ai}+v_{Af}=v_{Bi}+v_{Bf}

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45

center of mass distance

x_{com}=m_{1}x_{1}+m_{2}x_{2}/m_{1}+m_{2}

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46

velocity of center of mass

v_{com}=m_{1}v_{1}+m_{2}v_{2}/m_{1}+m_{2}

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47

acceleration of a harmonic oscilator (spring)

a=-(k/m)x

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48

angular frequency (rate of change of angular displacement)

ω=2πf

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49

period of an oscillating spring

T=2π√m/k

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50

period of an oscillating pendulum

T=2π√L/g

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51

max displacement of an oscillating spring (x_{max})

x_{max}=±A

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52

max velocity of an oscillating spring (v_{max})

v_{max}=±A√k/m

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53

max acceleration of an oscillating spring (a_{max})

a_{max}=±A(k/m)

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54

acceleration of a harmonic oscillator (pendulum)

a=(g/L)x

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55

torque formula

τ=F⊥r

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56

moment of inertia

I=Σmr²

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57

Newton’s second law of rotation

τ=Iα

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58

angluar momentum (L)

L=Iω

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59

rotational kinetic energy

K_{R}=1/2(Iω²)

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60

angular impluse-momentum

Στ⋅t=ΔL=Iω_{f}-Iω_{i}

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61

conservation of energy while rolling

U_{g}=K_{T}+K_{R}

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62

Unit of Force

Newton (N=kg⋅m/s²)

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63

Unit of Frequency

Hertz (Hz)

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64

Unit of Distance

Meter (m)

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65

Unit of Time

Second (s)

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66

Unit of Velocity

m/s

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67

Unit of Acceleration

m/s²

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68

Unit for Coefficient of Friction (μ)

No Units

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69

Unit for Angular Displacement

Rad

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70

Units for Angular Velocity

rad/s

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71

Units for Angular Acceleration

rad/s²

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72

velocity of an object in uniform circular motion (v)

v=2πr/T

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73

total acceleration of a rotating object (non-UCM)

a_{tot}=√a_{c}²+a_{t}²

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74

maximum velocity at which you can go around a circle

v≤√rgμ

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75

velocity of an object on a simple circular pendulum

v=√rgtanθ

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76

Unit of Energy

Joules (J=(kg⋅m²)/s²)

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77

Unit of Power

Watt (W=(kg⋅m²)/s³)

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78

Unit of Momentum

kg⋅m/s

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79

Unit for a spring constant (k)

N/m

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80

frequency formula

f=1/T

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81

angular velocity of an object oscillating on a pendulum

ω=√g/L

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82

Unit for Torque

N⋅m

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83

Newton’s second law (torque)

τ = mr^{2}α

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84

Unit for Angular Momentum (L)

kg⋅m²/s

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85

velocity of an object that starts at rest and ends at zero level (conservation of energy)

v=√2gh

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86

acceleration in an atwood’s machine

a=(m_{1}-m_{2})⋅g/m_{1}+m_{2}

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