A vector of magnitude $$10$$ N acting in $$XY-plane$$ has components $$8$$ N and $$6$$ N along positive $$X-axis$$ and positive $$Y-axis$$, respectively. The coordinate system is rotated about $$Z-axis$$ through angle $$90o$$ in $$anti-clockwise$$ direction. Find $$x-component$$ and $$y-component$$ in new coordinate system.

Question

Infinity Learn · Accepted Answer

In new coordinate system,Fsin⁡$$37$$∘$$=6NFcos$$⁡$$37$$∘$$=8Nx-component$$ $$Fx=Fsin$$⁡$$37$$∘$$=10$$×$$35=6Ny-component$$ $$Fy=$$−Fcos⁡$$37$$∘$$=$$−$$10$$×$$45=$$−$$8N$$

A vector of magnitude 10 N acting in XY-plane has components 8 N and 6 N along positive X-axis and positive Y-axis, respectively. The coordinate system is rotated about Z-axis through angle 90^o in anti-clockwise direction. Find x-component and y-component in new coordinate system.

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A vector of magnitude 10 N acting in XY-plane has components 8 N and 6 N along positive X-axis and positive Y-axis, respectively. The coordinate system is rotated about Z-axis through angle 90o in anti-clockwise direction. Find x-component and y-component in new coordinate system.

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Ready to Test Your Skills?

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A vector of magnitude 10 N acting in XY-plane has components 8 N and 6 N along positive X-axis and positive Y-axis, respectively. The coordinate system is rotated about Z-axis through angle 90^o in anti-clockwise direction. Find x-component and y-component in new coordinate system.