Equations for AP Physics 1 that you need to know that AREN’T on the formula sheet

Equations for AP Physics 1 that you need to know that AREN’T on the formula sheet

Cheatography
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Some physics formulas that will be useful in kinematics. Not a truly complete list of formulas though, as some things are missing.
I can’t think of any more formulas for this cheat sheet though, so suggestions on what to add would be helpful.

Table of Contents

Kinematics 2D Motion

V

0

= Initial velocity of object

V = Final velocity of object

a = Acceleration of object

t = Time

V

0

= Initial velocity of object

V = Final velocity of object

a = Acceleration of object

Δx / Δy = Change in position

Δx / Δy = Change in position

V

0

= Initial velocity

t = Time

a = Acceleration

F = ma

F = Force from object m = Mass of object a = Acceleration of object

F

f

= Force of friction

μ = Coefficient of friction

N = Normal force

Note: Some formulas may involve BOTH the x and y directions, as well as incorporate other formulas outside kinematics.

Momentum

FΔt = Δp = Impulse

m

V

= Final momentum

m

V0

= Initial momentum

m

Vbefore

– m

V0before

= m

Vafter

– m

V0after

Note: Momentum is ALWAYS conserved. You may need to note that the momentum before is equal to the momentum after.

Energy

W = Fd

W = Work done F = Force applied d = Distance travelled

W = Work done

m = Mass of object

V = Final velocity

V

0

= Initial velocity

U

g

= Work done by gravity

m = Mass

g = Gravity

h / d = Height or distance traveled

F

S

= Force of spring (Restored Force)

k = Spring coefficient

x = Distance from equilibrium

W

S

= Work done by spring

k = Spring coefficient

x = Distance from equilibrium

KE = ½mV2

KE = Kinetic Energy m = Mass v = Velocity of object

KE + U

g

+ U

S

=

KE + U

g

+U

S

+ W

KE = Kinetic Energy (is the object moving?)

U

g

= Work done by gravity (is the object above where you set x = 0?)

U

S

= Work done by spring (is a spring involved?)

W = Friction (did energy go to friction?)

Note: Energy is SOMETIMES conserved depending on the situation. Inelastic collisions cannot apply the conservation of energy because of the loss of energy. However, you can apply the conservation of energy for elastic collisions.

Rotational Motion

ω

0

= Angular initial velocity

ω = Angular final velocity

α = Angular acceleration

t = Time

ω

0

= Angular initial velocity

ω = Angular final velocity

α = Angular acceleration

θ = Angular change in position

θ = Angular change in position

ω

0

= Angular initial velocity

t = Time

α = Angular acceleration

V

T

= Tangential (Linear) velocity

r = Radius

ω = Angular final velocity

a

T

= Tangential (Linear) acceleration

r = Radius

α = Angular acceleration

a

C

= Centripetal acceleration

V

T

= Tangential (Linear) velocity

r = Radius

a

r

= Radial Acceleration

r = Radius

ω = Angular velocity

τ = Torque

F

⊥

= Perpendicular Forces

d= Distance from Pivot Point

I = Σmr^2

I = Moment of Inertia (Rotational Moment / Rotational Intertia) Σmr2 = Total of each Mass x Radius Squared

KE

C

= Kinetic Circular Energy

I = Moment of Inertia (Rotational Moment / Rotational Intertia)

ω = Angular velocity

τ = Iα

τ = Torque I = Moment of Inertia (Rotational Moment / Rotational Intertia) α = Angular acceleration

KE

R

= 1/2 I

P

ω

2

= 1/2(I

COM

+ mh

h

)ω

2

=1/2(m(V

COM

)

2

) + 1/2Iω

2

KE

R

= Kinetic Rolling Energy

1/2(m(V

COM

)

2

) = Sliding Equation

1/2Iω

2

= Rotation Equation

l = mrω

l = Momentum of a particle

L = Iω

L = Momentum of a rigid body (not a particle)

NOTE:
– You may need to consider that ω = dθ / dt and α = dω / dt.
– Account for all objects rotating the pivot point when calculating I.
– Momentum is ALWAYS conserved.