Question

A grampophone turn table rotating at an angular velocity 3rad/s,stops after one revolution .find the angular retardation

Answer 1

Initial Angular velocity , ω₀ = 3 rad/s
After one revolution , stops tbe rotation.
∴ final angular velocity , ω = 0 rad/s
And angular displacement = 1 revolution = 2π rad { 1 revolution means complete circle and we know angle of one complete circle is 360° or 2π rad }

Now, use formula
ω² = ω₀² + 2αθ, here α is the angular acceleration/retardation and θ is the angular displacement
∴ 0 = 3² + 2 × α × 2π
⇒ - 9 = 4π α
⇒ α = -9/4π = - 0.71656 rad/s²

Hence, angular retardation = 0.71656 rad/s²

Answer 2

Given :
Angular velocity= ω₀= 3rad/s

After one revolution the gramophone stops
So final angular velocity=ω=0 rad/s

Angular displacement =θ= 2π rad 

Formula to be used :

ω²=ω₀² + 2α θ

0=3² + 2 α π

-9=4απ

α= -9 /4π = -9/2x3.14 = -0.716 rad/s²

∴ Angular retardation=0.715 rad/s²