Normal modes in waves:

λ=

f=

(closed at one end)

=4L/n

=n*v/(4L)

(n=1,2,3...)

Normal Modes in Waves

λ=

f=

(open at both ends)

=2L/n

=n*v/(2L)

Doppler Shift

f'=

Angular Frequency of pendulum:

ω=

Period:

T=

=√(g/L)

=2π*√(L/g)

Period of a mass on a spring:

T=

Angular frequency:

ω=

=2π*√(m/k)

=√(k/m)

Period of circular/harmonic motion:

T=

=2π/ω

Bouyant force:

F_B=

=ρ_fluidgV

(V=volume of displaced fluid)

Variation of Pressure with depth:

P=

Escape velocity:

v_esc=

Kepler's Third Law:

T²⁼

=(4π²/(GM))*a³

(a= semimajor axis)

Angular Momentum:

L=

L_z=

=r x p

=mvrsinθ

=Iω

Torque:

τ=

=Iα

=dL/dt

=r x F

Parallel-Axis Theorem:

I=

Rotational KE:

T_R=

Moment of Inertia:

I=

=Σmr²

=∫r²dm

=∫ρr²dV

Angular Acceleration:

α=

=dω/dt

=a_T/r

Angular speed:

ω=

=dθ/dt

=v_T/r

Arclength:

s=

Center of Mass Position:

r_cm=

=1/M Σmr

=1/M ∫r dm

Impulse:

I=

=Δp

=∫F dt

Instantaneous Power:

P=

=dE/dt

=dW/dt

=F dr/dt

ΔE_mech=

(When non-conservative forces are present)

=-∑W_ncf

work:

W=

=F · r

=ΔKE

Centrepetal acceleration:

a_c=