A wheel is rotating at 1800 rpm about its own axis. When the power is switched off, it comes to rest in 2 minutes. Then the angular retardation in rad s-2 is

Question

A wheel is rotating at 1800 rpm about its own axis. When the power is switched off, it comes to rest in 2 minutes. Then the angular retardation in rad s-2 is (A) 2 π (B)  π (C) (π/2) (D) (π/4)

Tardigrade Admin · Accepted Answer

First equation of rotational motion ω=ω0+α t where ω =2 π n=2 π × (1800/60) =60 π rps ω0 =0 t =2 × 60=120 s 60 π =0+α × 120 α =(60 π/120) α =(π/2) rad / s 2

Q. A wheel is rotating at $1800 r p m$ about its own axis. When the power is switched off, it comes to rest in $2$ minutes. Then the angular retardation in $r a d s^{- 2}$ is

$2 π$

$π$

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{6}$

First equation of rotational motion
$ω = ω_{0} + α t$
where $ω = 2 πn = 2 π \times \frac{1800}{60}$
$= 60 π r p s$
$ω_{0} = 0$
$t = 2 \times 60 = 120 s$
$60 π = 0 + α \times 120$
$α = \frac{60 π}{120}$
$α = \frac{π}{2} r a d / s^{2}$

Q. A wheel is rotating at 1800rpm about its own axis. When the power is switched off, it comes to rest in 2 minutes. Then the angular retardation in rads−2 is

2π

π

2π​

4π​

6π​

First equation of rotational motion ω=ω0​+αt where ω=2πn=2π×601800​ =60πrps ω0​=0 t=2×60=120s 60π=0+α×120 α=12060π​ α=2π​rad/s2