Equations

speed/velocity

v_{avg} = \frac{\Delta s}{\Delta t}

v = \frac{\mathrm d}{\mathrm d t} {s}

acceleration

a_{avg} = \frac{\Delta v}{\Delta t}

a = \frac{\mathrm d}{\mathrm d t} {v}

equations of motion

v = {v}_{{0}}+a \cdot t

s = {s}_{{0}}+{v}_{{0}} \cdot t+\frac{1}{2} \cdot a \cdot t

v = \sqrt{{v}_{{0}}^{2}+2 \cdot a \cdot \left( s-{s}_{{0}} \right)}

v_{avg} = \frac{1}{2} \cdot \left( v+{v}_{{0}} \right)

Newton’s 2nd law

\sum F = m \cdot a

\sum F = \frac{\mathrm d}{\mathrm d t} {p}

weight

W = m \cdot g

friction

f \leq {\mu} \cdot N

centripetal acceleration

a_{c} = \frac{v^{2}}{r}

a_{c} = {{\omega}}^{2} \cdot r

momentum

p = m \cdot v

impulse

J = F_{avg} \cdot \Delta t

J = \int_{}^{} \! {F} \: \mathrm d {t}

impulse-momentum

F_{avg} \cdot \Delta t = m \cdot \Delta v

\int_{}^{} \! {F} \: \mathrm d {t} = \Delta p

work

W = F_{avg} \cdot \Delta s \cdot \cos \left( {\theta} \right)

W = \int_{}^{} \! {F} \: \mathrm d {s}

work-energy

F_{avg} \cdot \Delta s \cdot \cos \left( {\theta} \right) = \Delta {Ε}

\int_{}^{} \! {F} \: \mathrm d {s} = \Delta {Ε}

kinematic energy

K = \frac{1}{2} \cdot m \cdot v^{2}

general potential energy

\Delta U = \operatorname{-} \int_{} \! {F} \: \mathrm d {s}

gravitational potential energy

\Delta U_{s} = m \cdot g \cdot \Delta h

efficiency

{\eta} = \frac{W_{out}}{E_{in}}

power

P_{avg} = \frac{\Delta W}{\Delta t}

P = \frac{\mathrm d}{\mathrm d t} {W}

power-velocity

 P_{avg} = F_{avg} \cdot v \cdot \cos \left( {\theta} \right)

 P = F \cdot v

angular velocity

 {\omega}_{avg} = \frac{\Delta \theta }{\Delta t}

 {{\omega}} = \frac{\mathrm d}{\mathrm d t} {{\theta}}

 v = {{\omega}} \times r

angular acceleration

 {\alpha}_{avg} = \frac{\Delta {\omega}}{\Delta t}

 {\alpha} = \frac{\mathrm d}{\mathrm d t} {{{\omega}}}

 a = {\alpha} \times r-{{\omega}}^{2} \cdot r

equations of rotation

 {{\omega}} = {\omega}_{0}+{\alpha} \cdot t

 {\theta} = \theta_{{0}}+{\omega}_{0} \cdot t+\frac{1}{2} \cdot {\alpha} \cdot t

 {{\omega}} = \sqrt{{\omega}_{0}^{2}+2 \cdot {\alpha} \cdot \left( {\theta}-\theta_{0} \right)}

 {\omega}_{avg} = \frac{1}{2} \cdot \left( {{\omega}}+{\omega}_{0} \right)

2nd law of rotation

 \sum  \tau  = l \cdot a

 \sum  \tau  = \frac{\mathrm d}{\mathrm d t} {L}

torque

 {\tau} = r \cdot F \cdot \sin \left( {\theta} \right)

 {\tau} = r \times F

moment of inertia

 I = \sum  m \cdot r^{2}

 I = \int_{}{}{r^{2}} \: \mathrm d {m}

rotational work

 W = \tau _{avg} \cdot \Delta \theta

 W = \int_{}{}^{}{}{\tau} d {{\theta}}

rotational power

 P = {\tau} \cdot {{\omega}} \cdot \cos \left( {\theta} \right)

 P = {\tau} \cdot {{\omega}}

rotational kinetic energy

 K = \frac{1}{2} \cdot I \cdot {{\omega}}^{2}

angular momentum

 L = m \cdot r \cdot v \cdot \sin \left( {\theta} \right)

 L = r \times v

universal gravatation

 F_{g} =  \frac{G \cdot {m}_{{1}} \cdot {m}_{{2}}}{r^{2}}

gravitational field

 g =  \operatorname{-} \frac{G \cdot m}{r^{2}}

gravitational potential energy

 U_{g} =  \operatorname{-} \frac{G \cdot {m}_{{1}} \cdot {m}_{{2}}}{r}

gravitational potential

 V_{g} =  \operatorname{-} \frac{G \cdot m}{r}

orbital speed

 v = \sqrt{\frac{G \cdot m}{r}}

Escape speed

 v = \sqrt{\frac{2 \cdot G \cdot m}{r}}

Hooke’s law

 F =  \operatorname{-} k \cdot \Delta x

elastic potential energy

 U_{s} = \frac{1}{2} \cdot k \cdot \Delta x^{2}

simple harmonic oscillilation

 T = 2 \cdot {\pi} \cdot \sqrt{\frac{m}{k}}

simple pendulum

 T = 2 \cdot {\pi} \cdot \sqrt{\frac{l}{g}}

frequency

 f = \frac{1}{T}

angular frequency

 {{\omega}} = 2 \cdot {\pi} \cdot f

density

 {\rho} = \frac{m}{V}

pressure

 P = \frac{F}{A}

pressure in a fluid

 P = {P}_{{0}}+{\rho} \cdot g \cdot h

buoyancy

 B = {\rho} \cdot g \cdot V_{displaced}

mass flow rate

 q_{m} = \frac{m}{t}

volume flow rate

 q_{V} = \frac{V}{t}

mass continuity

 {\rho }_{{1}} \cdot {A}_{{1}} \cdot {v}_{{1}} = {\rho }_{{2}} \cdot {A}_{{2}} \cdot {v}_{{2}}

volume continuity

 {A}_{{1}} \cdot {v}_{{1}} = {A}_{{2}} \cdot {v}_{{2}}

Bernoulli’s equation

 {P}_{{1}}+{\rho} \cdot g \cdot {y}_{{1}}+\frac{1}{2} \cdot {\rho} \cdot {v}_{{1}}^{2} = {P}_{{2}}+{\rho} \cdot g \cdot {y}_{{2}}+\frac{1}{2} \cdot {\rho} \cdot {v}_{{2}}^{2}

dynamic viscosity

 \frac{F_{avg}}{A} = {\eta} \cdot \frac{\Delta v_{x}}{\Delta z}

 \frac{F_{avg}}{A} = {\eta} \cdot \frac{\mathrm d}{\mathrm d z} {v_{x}}

kinematic viscosity

 {\upsilon} = \frac{{\eta}}{{\rho}}

drag

 \frac{1}{2} \cdot {\rho} \cdot C \cdot A \cdot v^{2}

mach number

 Ma = \frac{v}{c}

Reynolds number

 Re = \frac{{\rho} \cdot {\upsilon} \cdot D}{{\eta}}

Froude number

 Fr = \frac{{\upsilon}}{\sqrt{g \cdot l}}

Young’s modulus

 \frac{F}{A} = E \cdot \frac{\Delta l}{{l}_{{0}}}

shear modulus

 \frac{F}{A} = G \cdot \frac{\Delta x}{y}

bulk modulus

 \frac{F}{A} = K \cdot \frac{\Delta V}{{V}_{{0}}}

surface tension

 {\gamma} = \frac{F}{l}

Resources

[downloads ids=”1406,1408″ columns=”2″ full_content=”no” excerpt=”no”]

[ihc-hide-content ihc_mb_type=”block” ihc_mb_who=”reg” ihc_mb_template=”-1″ ]Log in to download resources[/ihc-hide-content]

[ihc-login-form] [ihc-hide-content ihc_mb_type=”show” ihc_mb_who=”reg” ihc_mb_template=”-1″ ]

You have [mycred_my_balance wrapper=0 title_el=”” balance_el=””] tokens
Press here to buy more

[/ihc-hide-content]

Submit Content

Report a bug, typo, or inaccuracy

Earn 2 Tokens

per bug, limit of 6 Tokens per Day

Report a Bug
Submit an equation

Earn 3-5 Tokens

per equation, after review

Add Equation
Upload a resource

Earn 5-15 Tokens

per resource, after review

Upload Resource