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 $$900$$ in $$anti-clockwise$$ direction. Find $$x-component$$ and $$y-component$$ in new coordinate system.

Question

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 $$900$$ in $$anti-clockwise$$ direction. Find $$x-component$$ and $$y-component$$ in new coordinate system.

Infinity Learn · Accepted Answer

In new coordinate system,$$Fsin370=$$ $$6NFsin370=$$ $$6$$ NFcos $$370$$ $$=$$ $$8$$ $$Nx-component$$ Fx $$=$$ F $$sin370$$ $$=$$ $$10$$×$$35$$ $$=$$ $$6Ny-component$$ Fy $$=$$ $$-Fcos370$$                                 $$=$$ $$-10$$×$$45$$ $$=-$$ $$8$$ N

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 $90^{0}$ 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 900 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 $90^{0}$ in anti-clockwise direction. Find x-component and y-component in new coordinate system.