A constant torque of 100 Nm turns a wheel of moment of inertia about an axis passing through its centre. Starting from rest, its angular velocity after 3 s is [2023]

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Solution

Q.
A constant torque of 100 Nm turns a wheel of moment of inertia $300$ $kg$ $m^{2}$ about an axis passing through its centre. Starting from rest, its angular velocity after 3 s is [2023]

1 1 rad/s

2 5 rad/s

3 10 rad/s

4 15 rad/s

Ans.
(1)

With same analogy as $\vec{F} = m a$ we can write torque as,

$τ = I α or α = \frac{τ}{I} = \frac{100}{300} = \frac{1}{3} {rad/sec}^{2}$

Using equation of motion for rotational motion, $ω_{i} = 0$

$ω_{f} = ω_{i} + α t = 0 + \frac{1}{3} \times 3$

$ω_{f} = 1 rad/sec$

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