Question

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

• A. $4\text{s}$
• B. $2\text{s}$
• C. $8\text{s}$
• D. $10\text{s}$

Answer 1

The correct option is B $2\text{s}$

$I=1.2kg{m}^2;t=?$

$K_{rot}=1500J$

$\alpha =25\mathrm{rad}/s^2$

$\omega ={\omega }_0+\alpha t$
Initially the body was at rest, ${\omega }_o$=0

Rotational kinetic energy, $K=\frac{1}{2}I{\omega }^2\Rightarrow 1500=\frac{1}{2}\times 1.2\times w^2$

$w=\sqrt{\frac{3000}{1.2}}=50rad/s$

$\omega ={\omega }_0+\alpha t$
${\omega }_o=0$
$t=\frac{w}{\alpha }=\frac{50}{25}=2s$