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  4. The angular velocity of a body is overset arrow ω =2 hati+3 hatj+4 hatk and a torque overset arrow τ= hati+2 hatj+3 hatk acts on it. The rotational power will be

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Q. The angular velocity of a body is $\overset{ \rightarrow }{\omega }=2\hat{i}+3\hat{j}+4\hat{k}$ and a torque $\overset{ \rightarrow }{\tau}=\hat{i}+2\hat{j}+3\hat{k}$ acts on it. The rotational power will be

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

We know that
$P=\overset{ \rightarrow }{\tau}.\overset{ \rightarrow }{\omega }=\left(\hat{i} + 2 \hat{j} + 3 \hat{k}\right).\left(2 \hat{i} + 3 \hat{j} + 4 \hat{k}\right)$
$P=2+6+12=20 \, W$