A) \[{{\omega }_{1}}-{{\omega }_{2}}\]
B) \[\sqrt{\omega _{1}^{2}+\omega _{2}^{2}}\]
C) \[\sqrt{\omega _{1}^{2}-\omega _{2}^{2}}\]
D) \[{{\omega }_{1}}+{{\omega }_{2}}\]
Correct Answer: B
Solution :
Let is consider any two particles of the body. Let a particle of the first body rotate in the x-y plane in a circle of radius \[{{r}_{1}}.\] |
Similarly, let a particle of body 2 move in the y-z plane in a circle of radius \[{{r}_{2}}\]as shown in the figure. |
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Then \[{{\vec{\omega }}_{1}}={{\omega }_{1}}\hat{k}\] and \[{{\vec{\omega }}_{2}}={{\omega }_{2}}\hat{i}\] |
\[{{\vec{\omega }}_{21}}={{\vec{\omega }}_{2}}-{{\vec{\omega }}_{1}}={{\omega }_{2}}\hat{i}-{{\omega }_{1}}\hat{k}\] |
\[\therefore \,\,\,\left| \,{{{\vec{\omega }}}_{21}}\, \right|=\sqrt{\omega _{1}^{2}+\omega _{2}^{2}}\] |
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