Question

The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration.

Answer 1

Given:

n₁ = 15 r.p.s
n₂ = 5 r.p.s
No. of revolution = 50
As, ω = 2πn
ω = 2π x 5 = 10π
Also, ω₀ = 2πn₀ = 2π x 15 = 30π

Angular displacement in/revolution = 2π
Angular displacement in 50 revolution = 2 x 50π
                                                              = 100π

Now, ${\displaystyle {\omega }^2={\omega }_0^2+2\alpha \theta }$  
  ${\displaystyle {\left(10\pi \right)}^2={\left(30\pi \right)}^2+2\alpha \left(100\pi \right)}$
                     ${\displaystyle 900{\pi }^2-100{\pi }^2}$
${\displaystyle =-\alpha }$ =____________________________
                              ${\displaystyle 200\pi }$ 
${\displaystyle \alpha =-4\pi rad/s^2}$
Also, ${\displaystyle \alpha =-12.56 rad/s^2}$