First slide

Angular velocity, Angular acceleration

Question

A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming to be uniform? [KCET 2014]

Easy

A

$60 π {rads}^{- 2}$
B

$90 π rad s^{- 2}$
C

$2 π {rads}^{- 2}$
D

$40 π {rads}^{- 2}$

Solution

We know that, $ω = 2 π n$
Given, $n_{1} = 1800 rpm, n_{2} = 3000 rpm, Δ t = 20 s$
$ω_{1} = 2 π n_{1} = 2 π \times \frac{1800}{60} = 2 π \times 30 = 60 π rad / s$
Similarly, $ω_{2} = 2 π n_{2} = 2 π \times \frac{3000}{60} = 2 π \times 50 = 100 π rad / s$
If the angular velocity of a rotating wheel about an axis is changed by change in angular velocity in a time interval $Δ$ t, then the angular acceleration of rotating wheel about that axis is given by
$α = \frac{Change in angular velbcity}{Time interval}$
$= \frac{ω_{2} - ω_{1}}{Δ t} = \frac{100 π - 60 π}{20}$
$= \frac{40 π}{20} = 2 π {rads}^{- 2}$

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