Question 490: Centre of Mass and Rotational Motion

Question

What is the linear velocity if angular velocity $\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}$ and radius $\vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k})$ ?

Accepted Answer

$$ \begin{aligned} \vec{v} & =\vec{\omega} 	imes \vec{r}=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \ 3 & -4 & 1 \ 5 & -6 & 6 \end{array}ight| \ & =\hat{i}(-24+6)-\hat{j}(18-5)+\hat{k}(-18+20) \ \vec{v} & =-18 \hat{i}-13 \hat{j}+2 \hat{k} \end{aligned} $$

Answer

$(-30 \hat{\mathrm{i}}-13 \hat{\mathrm{j}}-38 \hat{\mathrm{k}})$

Answer

$(8 \hat{\mathrm{i}}-10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}})$

Answer

$\quad(-18 \hat{\mathrm{i}}-13 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})$

Answer

$(-2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})$

Centre of Mass and Rotational Motion

What is the linear velocity if angular velocity \vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k} and radius \vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k}) ?

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