First slide

Moment of intertia

Question

The moment of inertia of a body about a given axis is 1.2kgm²,Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500J,an angular acceleration of 25 rad s^{- 2} must be applied about that axis for a duration of

Easy

A

4 sec
B

2 sec
C

8 sec
D

10 sec

Solution

$E = \frac{1}{2} {Iω}^{2} or 1500 = \frac{1}{2} \times 1 \cdot 2 \times ω^{2}$
$∴ ω^{2} = \frac{3000}{1 \cdot 2} = 2500 or ω = 50 rad / \sec$
now, $t = \frac{ω}{α} = \frac{50}{25} = 2 \sec$

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