Physics: Uniform Circular Motion/ Oscillatory Motion Equations

Rotational motion equations

Newton’s Universal Law of Gravitation

F= G(mM)/r²

Centripetal Force

F_c= ma_c or F_c=m(v²/r) or F_c=m(rw²)

Centripetal Acceleration

a_c=v²/r or a_c=rw²

Angular Velocity

w=dtheta/dt or w=v/r

Frequency

f=1/T (number of oscillations per second)

Restoring Force

F= -kx, where k is the spring constant and x is the displacement from equilibrium.

Angular velocity and frequency

ω= 2pif

Solution to F=-kx

x=Acosωt, where A is the amplitude of oscillation, ω is the angular frequency, f is frequency of oscillation

Angular velocity and spring constant relationship

ω= sqrt(k/m), where k is the spring constant and m is the mass

Angular velocity and period

ω= 2pi/T

Frequency of mass on a spring

f= 1/2pi * sqrt(k/m)

Pendulum equation

T= 2pi *sqrt(L/g), where L is the length of the pendulum

String displacement equation

y(x,t)= Acos (kx±ωt), where kx is the wavelength, and ωt is the frequency

Spring constant and wavelength

k= (2pi)/λ

Speed of a wave

v=λf

Speed of wave on string

v= sqrt(F_t/u), where F_t is tension and u is (m/L)

Speed of sound

v_sound= sqrt(stiffness/density)

Intensity

I= power/area

Moment of inertia

I=mr²

Length and wavelength relationship

L=λ/2

Sound Intensity Level equation

β (dB) = 10 * log10 (I / I_O)

Doppler Effect Equation

f_obs= f_source((1±(v_obs/v_sound))/(1±v_source/v_sound)))