Question 591: Centre of Mass and Rotational Motion

Question

The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest. In order to produce rotational kinetic energy of $$1500 \mathrm{~J}$$, an angular acceleration of $$25 \mathrm{rad} / \mathrm{s}^2$$ must be applied about an axis for a time duration of

Accepted Answer

$$\begin{aligned} & \mathrm{I}=1.2 \mathrm{~kg}-\mathrm{m}^2, \quad 	ext { K.E. }=1500 \mathrm{~J}, \alpha=25 \mathrm{rad} / \mathrm{s}^2 \ & 	ext { K.E. }=\frac{1}{2} \mathrm{I} \omega^2 \ & 	herefore 1500=\frac{1}{2} 	imes 1.2 	imes \omega^2 \ & 	herefore \omega^2=\frac{2 	imes 1500}{1.2}=2500 \quad 	herefore \omega=50 \mathrm{rad} / \mathrm{s} \ & \quad \omega=\omega_0+\alpha \mathrm{t} \ & 	herefore 50=0+25 \mathrm{t}=25 \mathrm{t} \quad 	herefore \mathrm{t}=2 \mathrm{~s}\end{aligned}$$

Answer

8 s

Answer

2 s

Answer

4 s

Answer

1 s

Centre of Mass and Rotational Motion

The moment of inertia of a body about a given axis is $1.2 \mathrm{~kg} / \mathrm{m}^3. Initially the body is at rest. In order to produce rotational kinetic energy of 1500 \mathrm{~J}, an angular acceleration of 25 \mathrm{rad} / \mathrm{s}^2$ must be applied about an axis for a time duration of

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