Question

If the position vector of a particle is $\overset{\rightarrow}{r} = (3\widehat{i} + 4\widehat{j})$ meter and its angular velocity is $\overset{\rightarrow}{\omega} = (\widehat{j} + 2\widehat{k})$ rad/sec then its linear velocity is (in m/s)

• A. $(8\widehat{i} - 6\widehat{j} + 3\widehat{k})$
• B. $(3\widehat{i} + 6\widehat{j} + 8\widehat{k})$
• C. $- (3\widehat{i} + 6\widehat{j} + 6\widehat{k})$
• D. $(6\widehat{i} + 8\widehat{j} + 3\widehat{k})$

Answer 1

Answer: (A)

$(8\widehat{i} - 6\widehat{j} + 3\widehat{k})$

Answer 2

$\overset{\rightarrow}{v} = \overset{\rightarrow}{\omega} \times \overset{\rightarrow}{r}$

=$(3\widehat{i} + 4\widehat{j} + 0\widehat{k}) \times (0\widehat{i} + \widehat{j} + 2\widehat{k})$ $\overset{\rightarrow}{v} = \left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 3 & 4 & 0 \\ 0 & 1 & 2 \end{matrix} \right| = 8\widehat{i} - 6\widehat{j} + 3\widehat{k}$