Question

the angular displacement of an object having uniform circular motion is π/4 rad in every 3 sec. find its frequency of revolution

Answer 1

Given: ------------------------------------------------- Angular displacement= π/4  rad Time=3sec Frequency= v=? Angular velocity: ω=Angular displacement/ time =π/4×3  =π/12 rad/sec As we know that : ω= 2πv Where v is the frequency  Hence  v= ω/2π =π/2π×12 =1/24 hertz  Hence frequency is 1/24 sec

Answer 2

Given,

$d\theta=\frac{\pi}{4}\;rad\\\\dt=3\;sec\\\\\text{Angular Velocity}(\omega)=\frac{d\theta}{dt}\\\\\omega=\frac{\frac{\pi}{4}}{3}\\\\\omega=\frac{\pi}{12}\\\\Again,\\\\\omega=2\pi n\\\\\text{Where n is frequency}\\\\\omega=2\pi n\\\\n=\frac{\omega}{2\pi}\\\\n=\frac{\frac{\pi}{12}}{2\pi}\\\\n=\frac{1}{24}\;Hz$