First slide

Angular velocity, Angular acceleration

Question

The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in 14 s. Its angular acceleration is [NEET 2020]

Moderate

A

$2 π rad / s^{2}$
B

$28 π rad / s^{2}$
C

$120 π rad / s^{2}$
D

$1 rad / s^{2}$

Solution

Initial angular speed of wheel,
$ω_{0} = 2 π f_{0} = 2 π \times \frac{360}{60} rad / s = 12 π rad / s$
Final angular speed of wheel,
$ω = 2 π f = 2 π \times \frac{1200}{60} rad / s$
$= 40 π rad / s$
t = 14 s
From the equation of rotational motion, $ω = ω_{0} + α t$
$\Rightarrow α = \frac{ω - ω_{0}}{t} = \frac{40 π - 12 π}{14} = \frac{28 π}{14} = 2 π rad / s^{2}$

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